arXiv subjects

Sang Hu

Publications and source records attributed to Sang Hu.

5 recordsLinked to original sources

arXiv2026

Optimal exit strategies of CPT gamblers in unfair gambles

In this paper we study optimal exit strategies of gamblers with cumulative prospect theory (CPT) preferences in games where the expected payoff is strictly negative at each play, and formulate the problem as optimal stopping on asymmetric random walks. Applying a geometric transformation of the underlying cumulative gain/loss process, engaging randomized strategies and changing the decision variable from stopping times to probability distribution of the accumulated gain or loss at exit time, we solve the problem via the Skorokhod embedding. Drastically different from the fair gamble problem studied by He et al. (2019a), we show that the unfair problem in the infinite time horizon has finite values for a wide range of CPT parameter specifications. We then present the analytical solutions in the case of piece-wise power utility and power probability distortion functions. Compared to the strategies used in fair gambling, the CPT gamblers in unfair gambles are less loss-tolerant and choose not to gamble at all when the games are sufficiently unfavorable.

q-fin.MF↗

arXiv2025

Equilibrium Policy on Dividend and Capital Injection under Time-inconsistent Preferences

This paper studies the dividend and capital injection problem under a diffusion risk model with general discount functions. A proportional cost is imposed when injecting capitals. For exponential discounting as time-consistent benchmark, we obtain the closed-form solutions and show that the optimal strategies are of threshold type. Under general discount function which leads to time-inconsistency, we adopt the definition of weak equilibrium and obtain the extended HJB equation system. An explicit solution is derived under pseudo-exponential discounting where three cases of the dividend and capital injection thresholds are obtained. Numerical examples show that large capital injection cost may lead to no capital injection at all, while larger difference in group discount rate leads to higher equilibrium value function.

q-fin.MF↗

arXiv2024

From Time-inconsistency to Time-consistency for Optimal Stopping Problems

For optimal stopping problems with time-inconsistent preference, we measure the inherent level of time-inconsistency by taking the time needed to turn the naive strategies into the sophisticated ones. In particular, when in a repeated experiment the naive agent can observe her actual sequence of actions which are inconsistent with what she has planned at the initial time, she then chooses her immediate action based on the observations on her later actual behavior. The procedure is repeated until her actual sequence of actions are consistent with her plan at any time. We show that for the preference value of cumulative prospect theory, in which the time-inconsistency is due to the probability distortion, the higher the degree of probability distortion, the more severe the level of time-inconsistency, and the more time required to turn the naive strategies into the sophisticated ones.

econ.GN↗

arXiv2021

When to Quit Gambling, if You Must!

We develop an approach to solve Barberis (2012)'s casino gambling model in which a gambler whose preferences are specified by the cumulative prospect theory (CPT) must decide when to stop gambling by a prescribed deadline. We assume that the gambler can assist their decision using an independent randomization, and explain why it is a reasonable assumption. The problem is inherently time-inconsistent due to the probability weighting in CPT, and we study both precommitted and naive stopping strategies. We turn the original problem into a computationally tractable mathematical program, based on which we derive an optimal precommitted rule which is randomized and Markovian. The analytical treatment enables us to make several predictions regarding a gambler's behavior, including that with randomization they may enter the casino even when allowed to play only once, that whether they will play longer once they are granted more bets depends on whether they are in a gain or at a loss, and that it is prevalent that a naivite never stops loss.

q-fin.MF↗

arXiv2018

Two explicit Skorokhod embeddings for simple symmetric random walk

Motivated by problems in behavioural finance, we provide two explicit constructions of a randomized stopping time which embeds a given centered distribution $μ$ on integers into a simple symmetric random walk in a uniformly integrable manner. Our first construction has a simple Markovian structure: at each step, we stop if an independent coin with a state-dependent bias returns tails. Our second construction is a discrete analogue of the celebrated Azéma-Yor solution and requires independent coin tosses only when excursions away from maximum breach predefined levels. Further, this construction maximizes the distribution of the stopped running maximum among all uniformly integrable embeddings of $μ$.

math.PR↗