Ruin probability Dan Kucerovsky1 Department of Mathematics and Statistics University of New Brunswick Fredericton, New Brunswick, Canada Abstract We discuss studying ruin probability by Levy processes, and in particular the problem of approximat- ing them through compound sum of exponentials leads us to some interesting mathematical problems. Complex analysis and Weiner-Hopf factorization turn out to be useful tools. Email: [email protected] 1speaker 1 11 On the importance of data mining methods in actuarial science Shima Ara1, Saman Insurance Company, Tehran, Iran Abstract Nowadays, by rapid advancements in technology, the actuaries often encounter large amount of ob- servations from various insurance fields. Modeling and analyzing such big data raise several challenges in the application. In recent years, data mining methods attracted many interest in various fields, as well as insurance. Actuaries should be ready to combine their traditional knowledge with the data mining approach to deal with the new world of big data. In this talk, we will review the impact of these methods in actuarial science and present findings of employing such methods on life and nonlife insurance in Saman insurance company. 1speaker 1 12 Mortality modeling of skin cancer patients with actuarial applications Amin Hassan Zadeh1 Shahid Beheshti University, Tehran, Iran Raoufeh Asghari Shahid Beheshti University, Tehran, Iran Abstract In this article, the Markovian aging process is used to model mortality of patients with skin cancer. The time till death is assumed to have a phase-type distribution (which is defined in a Markov chain environment) with interpretable parameters. The underlying continuous-time Markov chain has one absorbing state (death) and nx +1 (x is the age when the patient is diagnosed with cancer) transient states. Each transient state represents a physiological age, and aging is transitions from one physiological age to the next one until the process reaches to its end. The transition can occur from any other state to the absorbing state. For patients with skin cancer in the United States, we estimate unknown parameters related to the aging process that can be useful for comparing the physiological age processes of patients with cancer and healthy people. For different age intervals, we estimate physiological age parameters for both males and females. The index of conditional expected physiological age of the patients with skin cancer at given ages are calculated and compared with the US total population. By using the bootstrap techniques, confidence bands and confidence intervals are constructed for the estimated survival curves and aging process parameters, respectively. The fitting results have been used for pricing the substandard annuities. Keywords: Aging process; mortality modeling; phase-type distribution; skin cancer; substandard annuities, boot- strap. 1speaker 1 13 A sample article title 1 Use of Decision Tree in Classifying Customers of Third-Party Liability Motor Insurance Farbod Khanizadeh1 Insurance Research Center, Tehran, Iran Mohammadreza Asghari Oskoei Allameh Tabataba'i University, Tehran, Iran Azadeh Bahador Insurance Research Center, Tehran, Iran Abstract The purpose of this study was to present a pattern through which insurance companies are enabled to classify the risk level of their customer and to predict the possibility of future claims. We have analyzed an insurance claim dataset provided by an Iranian insurance company with a sample size of 6000. According to the structure of the dataset, a supervised learning algorithm was used to describe the underlying relationships between variables. The proposed algorithm, decision tree, was implemented using Python programming language. Based on the results, age, vehicle type and marital status were the main three factors contributing in prediction of claims. Keywords: Decision Tree, Supervised Learning, Machine Learning, Classification, TPL. 1 Introduction Motor third party liability insurance (TPL) is a type of policy financially protecting third parties against both physical damage and bodily injury caused by car accidents. Under third party insurance Act , TPL is a compulsory insurance product in Iran. This is a sound reason for insurers to make an attempt to have their customers' risks assessed as accurately as possible. Furthermore, Iran insurance industry is going to experience the transition from auto-based TPL to the driver-based one [1]. Currently premiums are calculated solely according to auto features. By driver-based policies we mean the situation in which both drivers' and autos' characteristics would affect premium rates. The new regulations are going into effect by the end of 2021. Therefore, insurance companies need to review their risk assessment methods and make necessary amendments. In fact, in near future drivers’ traits will also play a crucial role in TLP ratemaking. Hence in this article we worked with a dataset of features describing both drivers and vehicles. Basically we built a model to classify customers based on their risk factors divided into demographic information and some significant properties of cars ([2], [3], [4], [5]). Decision tree is one of the common supervised learning algorithms used for both classification and regression. The method can be applied across a broad range of disciplines ([6], [7], [8], [9], [10], [11] ). Due to the nature of insurance industry, risk classification, decision tree has received considerable attention within this field ([12], [13], 1 speaker 14 Farbod Khanizadeh, Mohammadreza Asghari Oskoei, Azadeh Bahador [14], [15] ). The focus of this article was to develop a tree classifier to help insurers predict their high and low risk policyholders ([16], [17], [18]). Having gathered the data set, four steps were followed to build up the model: 1. Data preprocessing (replacing missing values, encoding categorical variables, split data into training and test set) 2. Build the tree classifier 3. Cross-validation and model evaluation 4. Avoid over-fitting (pre-pruning) 5. Model visualization Regarding step two, we used the "Gini Index" as a measure of node impurity. Basically in building the binary tree, Gini index is the splitting criterion at each node and would determine the importance of each feature. Gini index is defined as: 2 Gini= 1- ∑(Pi) Where Pi corresponds to the probability of each class. The next section would present key findings and outcomes of the research. Note that the learning algorithm was evaluated on a dataset containing information regarding TLP claims. In the given dataset there were 6000 observations for 5 features namely; policy holder age, type of vehicle, marital status, gender and the dependent variable claim with two levels (Yes/No). 2 Main results To obtain a reliable model we evaluated the accuracy of our classifier over both training and test sets. This was conducted through specifying the optimum value of a hyper parameter maximum depth of the tree. With the help of k-fold cross validation (for k=10) we tried thirty values for the depth and following figure was derived: As shown in the figure, accuracy reaches lower score as we increase the maximum depth of tree. The highest accuracy belongs to the first five values. Therefore, we pick the highest depth corresponds to the best accuracy score (i.e. max_depth=5). According to the above figure we have prevented a model from over-fitting via pre-pruning method. In fact the hyper parameter max_depth is used to set the maximum depth of our classifier. The following diagram depicts the decision tree of height 5: 15 Use of Decision Tree in Classifying Customers of Third-Party Liability Motor Insurance The model consists of 19 leaves which are terminal nodes and our tree starts with the most important features of the data set, the policyholder age. Furthermore the root consists of 4200 samples obtained based on the ratio between a training and validation sets (i.e. 70:30). As one can see the model is easy to interpret and enjoys high accuracy. Acknowledgment Authors are grateful for supports received from Iran Insurance Research Center (IRC). References [1] Compulsory Third Party Liability Insurance Damage due to Vehicle Accidents (2015) . [2] A.C. Yeo, K.A. Smith, R.J Willis, M. Brooks. Clustering technique for risk classification and prediction of claim costs in the automobile insurance industry. Intelligent Systems in Accounting, Finance & Management. 2001 Mar;10(1):39-50. [3] C.K Fan, W.Y. Wang. A comparison of underwriting decision making between telematics-enabled UBI and traditional auto insurance. Advances in Management and Applied Economics. 2017;7(1):17. [4] J. Son, M. Park, B.B. Park. The effect of age, gender and roadway environment on the acceptance and effectiveness of Advanced Driver Assistance Systems. Transportation research part F: traffic psychology and behaviour. 2015 May 1;31:12-24. [5] Y. Bian, C. Yang, J.L. Zhao, L. Liang. Good drivers pay less: A study of usage-based vehicle insurance models. Transportation research part A: policy and practice. 2018 Jan 1;107:20-34. [6] W.Y. Loh. Classification and regression trees. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery. 2011 Jan;1(1):14-23. 16 Farbod Khanizadeh, Mohammadreza Asghari Oskoei, Azadeh Bahador [7] C. Machuca, M.V. Vettore, M. Krasuska,S.R. Baker, P.G. Robinson. Using classification and regression tree modelling to investigate response shift patterns in dentine hypersensitivity. BMC medical research methodology. 2017 Dec;17(1):120. [8] Y.Y. Song, L.U. Ying. Decision tree methods: applications for classification and prediction. Shanghai archives of psychiatry. 2015 Apr 25;27(2):130. [9] V. Podgorelec, P. Kokol, B. Stiglic, I. Rozman. Decision trees: an overview and their use in medicine. Journal of medical systems. 2002 Oct 1;26(5):445-63. [10] L. E. Brandão, J.S. Dyer, W.J. Hahn. Using binomial decision trees to solve real-option valuation problems. Decision Analysis. 2005 Jun;2(2):69-88. [11] M. Zięba, S.K Tomczak, J.M. Tomczak. Ensemble boosted trees with synthetic features generation in application to bankruptcy prediction.