Portfolio Selections in P2P Lending: A Multi-Objective Perspective ∗ Hongke Zhao1 Qi Liu1 Guifeng Wang1 Yong Ge2 Enhong Chen1 1School of Computer Science and Technology, University of Science and Technology of China {zhhk, wgf1109}@mail.ustc.edu.cn {qiliuql, cheneh}@ustc.edu.cn 2Eller College of Management, University of Arizona, [email protected] ABSTRACT many users (i.e., borrowers and lenders) and generates mas- P2P lending is an emerging wealth-management service for sive lending transactions. For instance, the total loan is- individuals, which allows lenders to directly bid and invest on suance amount of Lendingclub had reached more than $13.4 the loans created by borrowers. In these platforms, lender- billion at the end of 2015. s often pursue multiple objectives (e.g., non-default prob- The prevalence of P2P lending and the availability of trans- ability, fully-funded probability and winning-bid probability) action data have attracted many researchers' attentions, which when they select loans to invest. How to automatically as- mainly focused on risk evaluation [23, 11], social relation sess loans from these objectives and help lenders select loan analysis [20, 13] and fully-funded analysis [28, 25]. Recently, portfolios is a very important but challenging problem. To authors in [34] proposed to study loan recommendations for that end, in this paper, we present a holistic study on portfo- lenders. However, due to the specific working mechanism of lio selections in P2P lending. Specifically, we first propose to P2P lending, the problem of loan/investment recommenda- adapt gradient boosting decision tree, which combines both tions in these platforms is still largely underexplored. static features and dynamic features, to assess loans from In P2P lending, there are mainly two kinds of roles: the multiple objectives. Then, we propose two strategies, i.e., borrowers who want to borrow money from others and the lenders who lend money to borrowers. Trading in these mar- weighted objective optimization strategy and multi-objective 3 optimization strategy, to select portfolios for lenders. For kets follows the Dutch Auction Rule [17, 31]. Specifically, each lender, the first strategy attempts to provide one opti- for borrowing money, a borrower will first create a listing mal portfolio while the second strategy attempts to provide to solicit bids from lenders by describing herself, the rea- a Pareto-optimal portfolio set. Further, we design two algo- son of lending (e.g., for wedding), the required amount (e.g., rithms, namely DPA and EVA, which can efficiently resolve $1,000) and the maximal interest rate (e.g., 10%). Then, if the optimizations in these two strategies, respectively. Fi- a lender wants to lend to this loan within its soliciting du- nally, extensive experiments on a large-scale real-world data ration (e.g., one week), a bid is created by describing both set demonstrate the effectiveness of our solutions. how much money she wants to lend (e.g., $50) and the min- imum interest rate (e.g., 9.5%). If this listing receives more Keywords than its required amount in its soliciting duration, those bids with lower rates will succeed/win, and other bids with high- P2P Lending; Portfolio Selection; Multi-objective Optimiza- er rates will be outbid/fail. In contrast, if this listing can't tion; Dynamic Feature receive enough bids in time, it would be expired and all the 1. INTRODUCTION previous bids would also fail [34, 6]. Based on this trading rule, a rational lender Alice may have the following two con- Recent years have witnessed the rapid development of on- siderations while selecting loans to bid. Multi-objective. 1 2 line P2P lending platforms, e.g., Prosper , Lendingclub . As While selecting loans, Alice may evaluate a loan from the a new emerging wealth-management service for individuals, probability of this loan being fully funded, the probability of P2P lending allows individuals to borrow and lend money winning the bid, as well as the loan risk (i.e., default prob- directly from one to another without going through any tra- ability) [4]. Portfolio. To be a successful lender, Alice also ditional financial intermediaries. Indeed, P2P lending has has the portfolio [24] perspective in her mind, i.e., she usual- become a fast growing investment market which attracts ly wants to select more than one loan (i.e., a portfolio) to bid ∗ in each investment. Indeed, some platforms (e.g., Prosper) Corresponding author. 1 already instruct lenders to diversify their money on multiple https://www.prosper.com/ 2 loans to reduce risk. However, it is difficult and boring for https://www.lendingclub.com/ Permission to make digital or hard copies of all or part of this work for personal or lenders to select dozens of loans in each time. Thus, devel- classroom use is granted without fee provided that copies are not made or distributed oping an automatic approach to recommend portfolios for for profit or commercial advantage and that copies bear this notice and the full cita- lenders is very needed. tion on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or re- In this paper, we present a holistic approach to help P2P publish, to post on servers or to redistribute to lists, requires prior specific permission lenders select investment portfolios, which can satisfy lender- and/or a fee. Request permissions from [email protected]. KDD ’16, August 13-17, 2016, San Francisco, CA, USA 3 There exists another kind of trading rule in P2P lending, in which c 2016 ACM. ISBN 978-1-4503-4232-2/16/08. $15.00 the platform determines posted rates for loans [31]. This trading can DOI: http://dx.doi.org/10.1145/2939672.2939861 be treated as a special case of our studied scenario. Table 1: Mathematical notations. Notation Description Historical Data Auction Data Loan VA = fv1; :::; vjVAjg the set of being-auctioned loans currently UA = fu1; :::; u g the set of current active lenders jUAj Historical Loans All Lenders Being-auctioned Loans Recent Bids x = (x1; :::; xjVAj) a selected loan portfolio u Lender Rei lender ui's preference on rate expectation v Dynamic Feature Extraction Active Lender Identification Rej loan vj 's declared interest rate in auction Multi-objective Pj = [Rj ;Tj ;Cj ] loan vj 's assessed profile Assessments Model Training …… GBDT αi = (αi1; αi2; αi3) lender ui's personalized weighted vector Assessment Models …… s' interest rate expectations, minimize investment risk (i.e., Offline Flow default probabilities) and maximize trading efficiency (i.e., Weighted Objective Strategy Multi-objective Optimization Strategy Portfolio fully-funded probabilities and winning-bid probabilities) si- A Portfolio A Portfolio Set Online Selections Flow multaneously. Specifically, we first identify active lenders DPA … EVA … …… in current market, i.e., the lenders who are most likely to in- vest in the following period, as our target users. Second, we Figure 1: Flowchart of portfolio selections. assess each being-auctioned loan from multi-objective views, importantly, we introduce how to assess being-auctioned loan- i.e., the non-default probability, fully-funded probability and s from multiple objectives. For better illustration, Table 1 winning-bid probability. Here, different from previous work- lists some mathematical notations used in this paper. s which only used static features in assessments, we also extract dynamic features of loans, and adapt an ensemble 2.1 Preliminaries method (i.e., Gradient Boosting Decision Tree) to combine Problem Statement. Formally, given the lenders' his- both static features and dynamic features to improve the torical bidding records, and current being-auctioned loans prediction performances. Finally, given the identified ac- VA = fv1; :::; vjVAjg in market, our goal is to select loan tive lenders and assessed loans, we attempt to select port- portfolios from VA for each active lender. Active lenders folios for each active lender. As we described above, the UA = fu1; :::; ujUAjg are those who are most likely to lend in selection should take into account multiple economic fac- the following period. A portfolio x = (x1; :::; xjVAj) is an op- tors/objectives, and the recommendation for each lender timal combination of multiple loans, if xj = 1, the j-th loan should also be portfolios rather than single loans. Specif- in VA is selected and put into the portfolio. For each lender ically, we propose two strategies, i.e., weighted objective op- ui 2 UA, the selected portfolios should satisfy her prefer- u timization strategy and multi-objective optimization strategy ence on rate expectation Rei with minimum risk (maximal to solve portfolio selections. Weighted objective strategy non-default probability) and maximum transaction efficien- combines three objectives into a single objective based on cy (fully-funded probability, winning-bid probability). a weighted objective vector, and provides each lender with Framework Overview. For tackling the above problem, an optimal portfolio. Multi-objective optimization strategy we propose a solution framework which is show in Figure 1. optimizes three objectives simultaneously and gets a Pareto- There are three major steps (brown backgrounds): (1) i- optimal solution set (portfolios) for each lender. For these dentifying the active lenders UA and learning their prefer- u two strategies, two efficient algorithms, i.e., DPA (dynamic ences on rate expectation Rei ; i 2 f1; :::; jUAjg; (2) assessing programming) and EVA (evolutionary algorithm), are de- each being-auctioned loan vj 2 VA on multiple objectives, signed to solve the optimization problems respectively. The (i.e., Non-default probability Rj , Fully-funded probability contributions of this paper can be summarized as follows. Tj , Winning-bid probability Cj ); and (3) selecting portfolios • To the best of our knowledge, this is the first work for all active lenders. on assessing loans from a multi-objective perspective We identify active lenders online (green arrows) and learn in P2P lending.