Research articles for the 2019-08-18

Hedging longevity risk in defined contribution pension schemes
Ankush Agarwal,Christian-Oliver Ewald,Yongjie Wang

Pension schemes all over the world are under increasing pressure to efficiently hedge the longevity risk posed by ageing populations. In this work, we study an optimal investment problem for a defined contribution pension scheme which decides to hedge the longevity risk using a mortality-linked security, typically a longevity bond. The pension scheme invests in the risky assets available in the market, including the longevity bond, by using the contributions from a representative scheme member to ensure a minimum guarantee such that the member is able to purchase a lifetime annuity upon retirement. We transform this constrained optimal investment problem into an unconstrained problem by replicating a self-financing portfolio of future contributions from the member and the minimum guarantee provided by the scheme. We solve the resulting optimisation problem using the dynamic programming principle and through a series of numerical studies reveal that the longevity risk has an important impact on the performance of investment strategies. Our results provide mathematical evidence supporting the use of mortality-linked securities for efficient hedging of the longevity risk.

Linear Stochastic Dividend Model
Sander Willems

In this paper we propose a new model for pricing stock and dividend derivatives. We jointly specify dynamics for the stock price and the dividend rate such that the stock price is positive and the dividend rate non-negative. In its simplest form, the model features a dividend rate that is mean-reverting around a constant fraction of the stock price. The advantage of directly specifying dynamics for the dividend rate, as opposed to the more common approach of modeling the dividend yield, is that it is easier to keep the distribution of cumulative dividends tractable. The model is non-affine but does belong to the more general class of polynomial processes, which allows us to compute all conditional moments of the stock price and the cumulative dividends explicitly. In particular, we have closed-form expressions for the prices of stock and dividend futures. Prices of stock and dividend options are accurately approximated using a moment matching technique based on the principle of maximal entropy.

Machine learning with kernels for portfolio valuation and risk management
Lotfi Boudabsa,Damir Filipovic

We introduce a computational framework for dynamic portfolio valuation and risk management building on machine learning with kernels. We learn the replicating martingale of a portfolio from a finite sample of its terminal cumulative cash flow. The learned replicating martingale is given in closed form thanks to a suitable choice of the kernel. We develop an asymptotic theory and prove convergence and a central limit theorem. We also derive finite sample error bounds and concentration inequalities. Numerical examples show good results for a relatively small training sample size.

Mislearning from Censored Data: The Gambler's Fallacy in Optimal-Stopping Problems
Kevin He

I study endogenous learning dynamics for people expecting systematic reversals from random sequences - the "gambler's fallacy." Biased agents face an optimal-stopping problem, such as managers conducting sequential interviews. They are uncertain about the underlying distribution (e.g. talent distribution in the labor pool) and learn its parameters from their predecesors. Agents stop when early draws are deemed "good enough," so predecessors' experience contain negative streaks but not positive streaks. Since biased agents understate the likelihood of consecutive below-average draws, society converges to over-pessimistic beliefs about the distribution's mean. When early agents decrease their acceptance thresholds due to pessimism, later agents will become more surprised by the lack of positive reversals in their predecessors' histories, leading to more pessimistic inferences and lower acceptance thresholds -- a positive-feedback cycle. Agents who are additionally uncertain about the distribution's variance believe in fictitious variation (exaggerated variance) to an extent depending on the severity of data censoring.

Social Contagion of Gift Exchange in Online Groups
Yuan Yuan,Tracy Liu,Chenhao Tan,Qian Chen,Alex Pentland,Jie Tang

Does receiving a gift encourage the recipient to send more gifts? Causal identification of behavioral contagion is very challenging, especially based on observational data from social networks. Given that the online monetary gift (also known as a "red packet") in WeChat groups is randomly split between group members, we are able to conduct a natural experiment to identify the causal effect of receiving online red packets on the contagion of gift exchange. Analyzing gifting behavior using a large-scale dataset of 3.4 million WeChat users, we find that recipients on average repay 18.29% of the amount they receive. Moreover, our analysis shows that recipients' contagion may be driven by different types of reciprocity. We further find that the "luckiest draw" recipients repay 1.5 times more than other recipients, and identify a group norm that luckiest draw recipients should send payment back to the group.