Behavioural Scoring and Retail Segmentation

Total Page:16

File Type:pdf, Size:1020Kb

Behavioural Scoring and Retail Segmentation Case Study Information Management Behavioural Scoring and Retail Segmentation www.saksoft.com | [email protected] INDIA | USA | UK | PARIS | SINGAPORE www.saksoft.com | [email protected] Basel II Solution Implementation The Basel II Accord The Basel II Accord aims to make international financial systems more stable and to put in Place incentives for banks to adopt better risk management practices. The information technology and systems changes implied by the Basel II Accord are the Largest and most expensive technology challenges faced by any financial service institution Background The client is one of the leading banks in Asia Pacific region, and provides a wide range of financial services including personal financial services, private banking, trust services, commercial and corporate banking, corporate finance, capital market activities, treasury services, futures broking, asset management, venture capital management, general insurance and life assurance. As part of their preparation for Basel II compliance, a data mart for Behavioural Scoring and Retail Segmentation was required. This data mart would store data for multiple countries. Saksoft built the Segmentation and Behavioural Scoring data mart for Singapore, Malaysia and Thailand. Requirement As per the IRB approach of the Basel II accord, banks are required to identify separately three sub-classes of exposures within the retail asset class category: Exposures secured by residential property Qualifying revolving retail exposures All other retail exposures After segmentation of the portfolio into the three distinct asset classes, banks must further segment them into homogeneous risk pools and estimate the corresponding loss characteristics (Probability of Default – PD, Exposure at Default- EAD and Loss Given Default – LGD) of each risk pool. The loss characteristic of each retail INDIA | USA | UK | PARIS | SINGAPORE www.saksoft.com | [email protected] pool will then be used as inputs for the Risk Weighted Assets (RWA) calculations for the retail portfolio and ultimately for the bank. Saksoft analysed the Country specific Business Requirements and identified the data elements that were to be extracted from the Global Data Warehouse for Scoring and Segmentation. All business exception conditions were identified at the product category level to ensure that all accounts were segmented into homogeneous risk pools. Behaviour scores predict the risk or profit of existing customers by employing statistical techniques to assess their transactions patterns to portray objective evaluation. Thus behaviour scores serve as a useful attribute for predicting risk. For the Singapore business of the customer, more than 500 variables for unsecured products were derived in the data mart (primarily delinquency, spend and payment related variables), which served as the source criteria for determining the behavioural scores. An interface was built with an external credit-scoring engine that would calculate the behaviour scores, which would be sent back to the data mart. Behaviour scores is an important driver for segmentation of products for all countries. Segmentation was done at various levels starting from the product level. For example: the credit cards portfolio was segmented by Vintage, Race, Behaviour Scores, Delinquency attributes and Utilization rates. Secured Overdrafts were segmented by vintage and collateral type. A set of financial products associated with a facility was grouped together as a “Financial Package” and segmented on multiple drivers like account conduct, account vintage and financial packages secured by rented property, commercial property etc. Risk drivers for PD, EAD and LGD were identified. PD is defined as a bank’s own internally generated estimate of the probability (expressed in decimals) that a particular obligor will default on its obligations to the bank over a given time period (usually one year). This was calculated for each segment (risk pool) as Number of defaults observed within the year/ Number of accounts in the reference pool. Data measures required for determining the probability of default included Max number of days OD in Excess over last 12 months; Number of outward cheques returned over last 12 months; Average utilization rate on credit cards over last 12 months; Average Sales coverage (funded working capital) over last 12 months; debt serviceability etc. LGD was calculated for each risk pool as Final Loss/ Loss outstanding at default, this is the estimated amount of loss that a bank would suffer if the obligor of a particular asset were to default on its obligations to the bank as a proportion of the overall amount of the bank’s exposure to the obligor for that asset. The Exposure at Default (EAD) is the estimated amount of facility outstanding (including potential additional draw down for committed facilities) at the point of default. This is the estimated amount of a bank’s gross exposure to an obligor in respect of a particular asset, should he default. EAD _EFF was calculated at the risk pool level as Current Outstanding + CCF (Credit Conversion Factor)* Undrawn Amount. Expected loss % was calculated as EL / EAD_EFF; where Expected Loss (EL) represents the cost of doing business, and is the amount of credit loss that the Bank expects to experience over a chosen time horizon. The SBS data mart, while having a common design structure, also included country specific business requirements based on country processes and local legal and regulatory requirements. INDIA | USA | UK | PARIS | SINGAPORE www.saksoft.com | [email protected] For example, For Malaysia, for credit cards, the retail segmentation process was executed on a daily basis, with outstanding balances and utilization being computed on a daily basis. This is different from Singapore and Thailand, where utilization was determined on a cyclical and on a month end frequency. For Thailand, specific changes included calculation of the NPL status (Non-Performing Loan) status at the customer level, as opposed to NPL status at the account level. Also Parent Child limits were defined at the customer level and individual exposures were calculated based on the Parent-child hierarchy. The Solution Saksoft built reports for Credit Scoring and Basel 2 segmentation metrics for Singapore, Malaysia and Thailand. Credit Scoring reports compared the statistics of development sample for credit scoring with the actual population, Population Stability Index and KS statistic related reports, and delinquency analysis vis-a–vis credit scoring etc. Another report displayed the Scorecard of various applications based on the Final Decision. Reports on population segmentation include Retail IRB Analysis for NPL and Non NPL accounts for multiple products, Population Distribution by Segmentation for multiple products, and tracking key metrics like Expected Loss, Expected Loss %, Risk Weighted Assets for multiple products over a period of time. Other reports include a Pool Migration Report that tracked product performance from one delinquency pool to the next, to NPL categorisation for multiple products, based on account vintages. There was also Back Testing Report, which tracked the last 12-month performance of the Ever-NPL accounts. A common universe was built for a single set of reports. To achieve better maintenance and improved performance of the universe, it was designed in such-a-way that all the common objects required for various reports were placed in a single class. The Technology The technology environment is as follows: GDW: DB400 V5R2 – Development is on client running in Windows platform, connectivity through DB2 Connect. Informatica Powercenter v6.1 on RS6000 (AIX) – Development on Windows platform clients. Oracle v9.2 on AIX Unix Server as temporary working area Data mart modeling using ER-Win 4.0 Connect: Direct for file exchange between different servers Control-M scheduler Reports on Business Objects 6.5 INDIA | USA | UK | PARIS | SINGAPORE www.saksoft.com | [email protected] .
Recommended publications
  • NLC-RISC 2019 Next Generation Investment Strategies for Risk Pools
    NEXT GENERATION INVESTMENT STRATEGIES FOR RISK POOLS DAN SMERECK, MANAGING DIRECTOR WHY INVESTMENT MATTERS FOR RISK POOLS? PURPOSE • INVESTMENT INCOME: • IS A CORNERSTONE TO THE RISK TRANSFER BUSINESS MODEL, AND MAXIMIZING INVESTMENT INCOME CAN MEAN THE DIFFERENCE BETWEEN REMAINING COMPETITIVE OR LOSING MEMBERS TO AGGRESSIVE PRICING. •HOW MUCH CAN YOU EXPECT TO EARN? •HOW MUCH RISK ARE YOU WILLING TO PRUDENTLY TAKE? APPROACH • INVESTMENT PERFORMANCE OBJECTIVES: WHAT IT TAKES TO EARN 7.5% ANNUALIZED WHAT TO EXPECT TO EARN 7.5% ANNUALIZED INCOME VS. PRICE RETURN YIELD + PRICE = BOND RETURNS REGULATORY REGIMES •FLEXIBLE VS. INFLEXIBLE •REGULATED VS. UNREGULATED •OPPORTUNITY COSTS & IMPLICATIONS FLEXIBLE VS. INFLEXIBLE INFLEXIBLE FLEXIBLE • U.S. TREASURY BONDS/NOTES • ALL “INFLEXIBLE” ITEMS PLUS: • U.S. AGENCY BONDS • INVESTMENT GRADE CORPORATE BONDS • FDIC INSURED CDS • MORTGAGE BONDS • ASSET-BACKED BONDS • HIGH YIELD BONDS • EQUITIES • INSURANCE REGULATIONS ORSA IS COMING FOR YOU… ORSA = “Own Risk & Solvency Assessment” Testing - NAIC OPPORTUNITY COST - INCOME $ 50,000,000 Portfolio Size 1 Year 3 Years 5 Year 10 Year 20 Year US Treasury 1-3 Year $ 1,540,000 $ 1,591,595 $ 2,524,493 $ 5,615,092 $ 37,370,882 Barclays U.S. Aggregate $ 2,645,000 $ 2,904,493 $ 6,763,842 $ 22,043,547 $ 75,525,857 Additional Income $ 1,105,000 $ 1,312,898 $ 4,239,349 $ 16,428,455 $ 38,154,975 85% Barclays Aggregate / 15% S&P 1500 $ 3,215,000 $ 5,951,673 $ 10,628,195 $ 35,326,303 $ 87,027,421 Additional Income $ 1,675,000 $ 4,360,078 $ 8,103,703 $ 29,711,211 $ 49,656,539
    [Show full text]
  • On the Efficiency of Pseudo Risk Pools and Proxy Yield Data on Crop
    On the Efficiency of Pseudo Risk Pools and Proxy yield data on Crop Insurance and Reinsurance in U.S Sebastain N. Awondo Alabama Center for Insurance & Information Research (ACIIR) Culverhouse College of Commerce, The University of Alabama Tuscaloosa, AL 35487,[email protected] Don W. Shurley Department of Agricultural & Applied Economics, The University of Georgia, Tifton, GA 31793, [email protected] Selected paper prepared for presentation at the 2017 Agricultural & Applied Economics Association Annual Meeting, Chicago, Illinois, July 30-August 1 1 1Copyright 2017 by Sebastain N. Awondo and Don Shurley. All rights reserved. Readers may make verbatim copies of this document for non-commercial purposes by any means, provided that this copyright notice appears on all such copies. Abstract We empirically investigate the impact of aggregated county risk pools , used as proxy for a county with limited data, on premium rates and reinsurance needs for crop revenue insurance in the U.S. To quantify systemic risk, we employ nested Archimedean copula-based models which relaxes the exchangeability restriction and less prune to curse of dimensionality inherent in copula-based models. In the first stage of our analysis, employing irrigated and non-irrigated cotton yields from seven counties in Texas, we derive `true' county-level rates using `unlimited' data. In the second stage, we derive rates based on proxy data aggregated over county risk pools. Finally we compare the `true' rates with those based on proxy data using root mean squared error (rmse) and diversification effect (DE). The results show substantial differences in systemic risk across risk pools. The risk pool use in practice was found to be far less efficient resulting to significantly high premiums rates and subsidies levels.
    [Show full text]
  • Marketplace Plan Payment Options for Dealing with High-Cost Enrollees
    NBER WORKING PAPER SERIES MARKETPLACE PLAN PAYMENT OPTIONS FOR DEALING WITH HIGH-COST ENROLLEES Timothy J. Layton Thomas G. McGuire Working Paper 22519 http://www.nber.org/papers/w22519 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 August 2016 This research was supported by NIMH R01-MH094290 and the Laura and John Arnold Foundation. The authors are grateful to Savannah Bergquist, Jeannie Biniek, Michael Chernew, Michael Cohen, Kelly Drury, Randy Ellis, Jeff Grant, Laura Hatfield, John Hsu, Amanda Kreider, Joseph Newhouse, Cassandra Peitzman, Sherri Rose, Anna Sinaiko, Richard van Kleef, Rene van Vliet and Wynand van de Ven for helpful discussion. Jeannie Binniek and Amanda Kreider provided excellent research assistance. The views in this paper are the authors’ own. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications. © 2016 by Timothy J. Layton and Thomas G. McGuire. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Marketplace Plan Payment Options for Dealing with High-Cost Enrollees Timothy J. Layton and Thomas G. McGuire NBER Working Paper No. 22519 August 2016 JEL No. I11,I13,I18 ABSTRACT Two of the three elements of the ACA’s “premium stabilization program,” reinsurance and risk corridors, are set to expire in 2017, leaving risk adjustment alone to protect plans against risk of high-cost cases.
    [Show full text]
  • Cooperative Insurance in Small-Holder Aquaculture Systems
    Received: 31 January 2018 Resilience through risk Revised: 18 June 2018 Accepted: management: cooperative 13 September 2018 Cite as: James R. Watson, insurance in small-holder Fredrik Armerin, Dane H. Klinger, Ben Belton. Resilience through risk aquaculture systems management: cooperative insurance in small-holder aquaculture systems. Heliyon 4 (2018) e00799. a,∗ b c d James R. Watson , Fredrik Armerin , Dane H. Klinger , Ben Belton doi: 10 .1016 /j .heliyon .2018 . e00799 a Oregon State University, College of Earth, Ocean and Atmospheric Sciences, Corvallis, USA b Department of Real Estate and Construction Management, KTH Royal Institute of Technology, Stockholm, Sweden c Center on Food Security and the Environment, Stanford University, Stanford, CA, USA d Department of Agricultural, Food, and Resource Economics, Michigan State University, East Lansing, USA * Corresponding author. E-mail address: [email protected] (J.R. Watson). Abstract Aquaculture is a booming industry. It currently supplies almost half of all fish and shellfish eaten today, and it continues to grow faster than any other food production sector. But it is immature relative to terrestrial crop and livestock sectors, and as a consequence it lags behind in terms of the use of aquaculture specific financial risk management tools. In particular, the use of insurance instruments to manage weather related losses is little used. In the aquaculture industry there is a need for new insurance products that achieve both financial gains, in terms of reduced production and revenue risk, and environmental wins, in terms of incentivizing improved management practices. Here, we have developed a cooperative form of indemnity insurance for application to small-holder aquaculture communities in developing nations.
    [Show full text]
  • Brief 4: Risk-Pooling Mechanisms
    Immunization Financing Toolkit The World Bank and GAVI Alliance December 2010 Brief 4: Risk-Pooling Mechanisms What is risk pooling? Risk pooling is also known as health insurance, which is a group of persons contributing to a common pool, usually held by a third party. These funds are used to pay for all or part of the cost of providing a defined set of health services for members of the pool. In low- and middle-income countries, there are relatively high out-of-pocket expenditures for health care services. Families may go into debt and sell critical assets in order to finance health services. Risk pooling is the collection and management of financial resources so that large, unpredictable individual financial risks become predictable and are distributed among all members of the pool. Risk pooling can provide financial protection to households in the face of high health care costs. What are the different types of risk-pooling mechanisms available? There are several different types of risk-pooling mechanisms that can be used to support and finance immunization services. National insurance systems: Funding comes from general revenues and medical coverage is provided to the entire population for a fixed set of services (benefits package). Services are delivered through a network of public (and NGO) providers. Social health insurance systems: Funding comes from mandatory, earmarked payroll contributions from individuals and employers. Coverage is provided to contributors, usually in a phased manner. Services are provided based on a defined benefits package that can include immunization services. Additional subsidies may come from external assistance or earmarked taxes.
    [Show full text]
  • Risk-Pooling – Necessary but Not Sufficient? Philip Davies1 & Guy Carrin2
    Editorial Risk-pooling – necessary but not sufficient? Philip Davies1 & Guy Carrin2 The search for a ‘‘good’’ health system realizing the benefits of risk-pooling in planned programme of mergers, to form is constant. Even in countries where countries without the organizational capa- ever larger risk pools. Such an approach comprehensively organized national health city to operate formal schemes on a national could allow infrastructure and other cap- systems have existed for over a century, level. Risk-pooling, on any scale, has its abilities to develop over time, and may the debate on how best to design them to downside, however. Clients who are eventually lead to the emergence of a single ensure the effective financing, organization insured and therefore do not have to pay regional (or national) risk pool which and provision of care is as lively and the full cost of services may be inclined many would consider to be the ideal. controversial as ever. to over-use those services, while providers In addition, attempts to employ risk- During the last quarter of the may be happy to let them do so because it pooling will fail if they do not have the 20th century many countries proposed a enables them to earn more (moral hazard). confidence of the people they seek to serve. wide variety of sweeping reforms, some In addition, those who are more likely to Any pooling scheme will be judged by its of which were adopted and refined, and require care have a stronger incentive to join results, and if problems of access or others rejected.
    [Show full text]
  • Risk-Sharing Pools Have Surpassed Commercial Insurance for Public
    Risk-sharing pools have surpassed commercial insurance for public entities – cities, counties, schools, and others – because they demonstrate effective government collaboration. Partnership. Local public entities form risk pools to reduce and stabilize long-term insurance costs and ensure access to the coverage and service needed for critical local government functions such as public safety, education, roads and transportation, and more. History Public entities created pools beginning in the early 1970s after most commercial insurers abandoned the public entity market. At that time, and again in the mid-1980s, commercial insurers responded to changing risks local governments faced – trends that made this market less profitable. Pools emerged as the stabilizing force the public sector needed. Today, pools are the source of innovation public entities need to address continuing challenges in risk management, even as the insurance crisis has calmed. Pooling is best embodied in a Swedish proverb: The best place to find a helping hand is often at the end of your own arm. © 2014 AGRiP Current status It is estimated that there are over 500 risk-sharing pools serving municipalities, school districts, and other public entities in the United States and Canada, and pools are emerging around the world. Although public-entity risk pools typically share common values and core purposes, each pool is unique, with features that reflect both their members' priorities and their states' traditions, laws, and regulations. There are more than 90,000 public entities in the United States. The Association of Governmental Risk Pools (AGRiP) estimates that at least 80 percent of all local public entities participate in one or more risk pools.
    [Show full text]
  • Fact Sheet 6: Pooling and Mutual Options for Public Assets Insurance
    DRAFT WORKING PAPER FOR SEADRIF WEBINAR SEADRIF Knowledge Series: Financial Protection of Public Assets Fact Sheet 6: Pooling and Mutual Options for Public Assets Insurance 0 The SEADRIF Knowledge Series: Financial Protection of Public Assets This sixth fact sheet1 is part of a Knowledge Series that supports government officials as they develop their understanding of the steps needed to design, develop, deliver, and operate effective financial protection of public assets, particularly through risk transfer and insurance. The Knowledge Series encompasses an end-to-end development of public asset financial protection and insurance, as shown in figure 1. See previous fact sheets in this series for a more detailed introduction. Each fact sheet will cover a major element of the process and will highlight considerations to assist government officials and other stakeholders who are tasked with developing solutions. New terminologies are defined in the glossary. Figure 1. Overview of the Knowledge Series 1 Drafted by Lit Ping Low, Greg Fowler, Rob Antich, and Nicola Ranger, with inputs from John Plevin and Benedikt Signer. The draft will be refined and finalized after the series of SEADRIF webinars about public asset financial protection, and it will build on feedback from the SEADRIF members and other webinar participants. The findings, interpretations, and conclusions expressed in this fact sheet do not necessarily reflect the views of the World Bank, its board of executive directors, or the governments they represent. The World Bank does not guarantee the accuracy of the data included in this work. An ASEAN+3 Initiative in partnership with The World Bank 1 Introduction This fact sheet considers how governments can use risk pooling and mutualization to support large-scale programs on public asset insurance in addition to, or as an alternative to, insurance and alternative risk-transfer markets (discussed in more detail in Fact Sheet 5).
    [Show full text]
  • The Merits of Pooling Claims: Mutual Vs. Stock Insurers
    THE MERITS OF POOLING CLAIMS: MUTUAL VS. STOCK INSURERS CAROLINA OROZCO-GARCIA HATO SCHMEISER WORKING PAPERS ON RISK MANAGEMENT AND INSURANCE NO. 197 EDITED BY HATO SCHMEISER CHAIR FOR RISK MANAGEMENT AND INSURANCE APRIL 2018 The merits of pooling claims: Mutual vs. stock insurers Abstract This paper aims to identify combinations of premiums, equity capital contributions, ruin probabilities, and pool sizes, under which a risk-averse policyholder, with an exponential utility function, is indifferent between purchasing insurance coverage with a mutual or a shareholder insurance company. In a mutual company, and in contrast to the shareholder insurer, the amount of premiums charged do not influence the policyholder's utility level. For the shareholder company, we analyze combinations of premiums and equity within a fixed pool size, such that a policyholder is indifferent to either of the two legal forms in focus. In addition, we include the restriction of a fixed ruin probability in the mutual and shareholder insurance company. A numerical illustration shows that given a fixed ruin probability, a determined pool size and fair premiums (i.e., the premium equals the expected indemnity payments), policyholders in the shareholder company experience higher utility levels than policyholders in a mutual insurance company. Hence, a risk-averse policyholder accepts an unfair premium in the shareholder company to obtain the same utility level as provided by the mutual company. 1 Introduction The term "risk pooling" in insurance is commonly used to refer to the spreading of risk among a large number of participants in a portfolio to reduce the impact of losses on the individual's wealth position (Smith & Kane, 1994; Albrecht, 1984; Albrecht & Huggenberger, 2017).
    [Show full text]
  • Moral Hazard, Risk Sharing, and the Optimal Pool Size
    Moral hazard, risk sharing, and the optimal pool size∗ Frauke von Bieberstein,y Eberhard Feess,z José F. Fernando,§ Florian Kerzenmacher,{ and Jörg Schillerk September 7, 2016 Abstract In risk pools, the effective share of the own loss borne is the sum of the direct share (the coinsurance rate) and the indirect share borne by the residual claimant. In a model with n identical risk-averse individuals and moral hazard, we derive two main results: First, for all mixed risk averse utility functions, the effective share required for incentive compatibility for the high effort increases in the pool size. This is a downside of larger pools as it, ceteris paribus, reduces risk sharing. Second, however, we find that the optimal pool size nevertheless converges to infinity as the positive effect from better diversification of the risk borne by other individuals always outweighs the negative effect from the larger risk of own damage. In our basic model, we restrict attention to two effort levels, but we show that our results extend to a model with continuous effort choice. Keywords: risk sharing, moral hazard, mutuals, partnerships JEL Classification: D81, G22 ∗We thank Harris Dellas, Marc Möller, Martin Nell, Richard Peter, and Harris Schlesinger for valuable comments. yUniversity of Bern, IOP, Engehaldenstr. 4, 3012 Bern, Switzerland, [email protected]. zFrankfurt School of Finance & Management, Sonnemannstr. 9-11, 60314 Frankfurt, Germany, [email protected]. §Universidad Complutense de Madrid, Facultad de Matemáticas, Departamento de Álgebra, Plaza de Ciencias, 3, 28040 Madrid, Spain, [email protected] {Frankfurt School of Finance & Management, Sonnemannstr. 9-11, 60314 Frankfurt, Germany, [email protected].
    [Show full text]
  • Methods of Risk Pooling in Business Logistics and Their Application
    Methods of Risk Pooling in Business Logistics and Their Application I n a u g u r a l d i s s e r t a t i o n zur Erlangung des akademischen Grades „Doktor der Wirtschaftswissenschaften“ (Dr. rer. pol.) eingereicht an der Wirtschaftswissenschaftlichen Fakultät der Europa-Universität Viadrina in Frankfurt (Oder) im September 2010 von Gerald Oeser Frankfurt (Oder) “Uncertainty is the only certainty there is, and knowing how to live with insecurity is the only security.” John Allen Paulos, Professor of Mathematics at Temple University in Philadelphia To my brother, who never failed to support me Acknowledgements First and foremost I would like to express my gratitude to my Ph.D. advisor Prof. Dr. Dr. h.c. Knut Richter, Chair of General Business Administration, especially Industrial Management, European University Viadrina Frankfurt (Oder), Germany for his extensive mentoring. He also kindly gave me the opportunity of gaining experience in teaching grad- uate courses in addition to my research. For willingly delivering his expert opinion on my thesis as the second referee I thank Prof. Dr. Joachim Käschel, Professorship of Production and Industrial Management, Tech- nical University Chemnitz, Germany very much. I would also like to gratefully acknowledge the support of all employees of Prof. Rich- ter's chair, especially Dr. Grigory Pishchulov: Among other things, he helped me carry out the “Subadditivity Proof for the Order Quantity Function (5.1)” in Appendix E mathemati- cally formally correctly. Furthermore, I thank Prof. Dr. Dr. h.c. Werner Delfmann, Director of the Department of Business Policy and Logistics, University of Cologne, Germany for the opportunity offered and for showing me that the world cannot be explained by mathematics alone.
    [Show full text]
  • Optimal Risk Pools Under Changing Volatility and Heterogeneous Risk Classes
    Optimal Risk Pools under Changing Volatility and Heterogeneous Risk Classes Florian Klein, Hato Schmeiser∗ July 5, 2018 Abstract We extend previous research into risk pooling by introducing a default probability driven premium loading as well as a relation between the premium level and demand through a convex price-demand function. Furthermore, we compare the profitability of a single risk pool for heterogeneous risk classes with multiple risk pools from the perspective of an insurer's shareholders using net present value cal- culus. In addition, we contrast multiple risk pools structured as a single legal entity with the case of multiple legal entities. To achieve the net present value maximizing default probability, the insurer adjusts the underlying equity capital. In this context, we demonstrate with our theoretical consid- erations and numerical examples that multiple risk pools with multiple legal entities are optimal if the equity capital must be decreased. An equity capital increase implies that multiple risk pools in a single legal entity are generally optimal. Moreover, a single risk pool for multiple risk classes rela- tively improves in relation to multiple risk pools with multiple legal entities whenever the standard deviation of the underlying claims increases. Keywords: Risk Pooling, Legal Entity, Default Probability, Price-Demand Function, Heterogeneous Risk Classes JEL classification: G22; G28; G32 1 Introduction Risk pooling is widely acknowledged as the core of insurance activity. Previous research analyzes a decreasing
    [Show full text]