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On penalized goal-reaching probability minimization under borrowing and short-selling constraints

Part of: Mathematical finance Applications Stochastic systems and control

Published online by Cambridge University Press:  05 November 2024

Ying Huang  and
Jun Peng
Ying Huang*
Affiliation:
Central South University
Jun Peng*
Affiliation:
Central South University
*
*Postal address: School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, P.R. China.
*Postal address: School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, P.R. China.
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Abstract

We consider a robust optimal investment–reinsurance problem to minimize the goal-reaching probability that the value of the wealth process reaches a low barrier before a high goal for an ambiguity-averse insurer. The insurer invests its surplus in a constrained financial market, where the proportion of borrowed amount to the current wealth level is no more than a given constant, and short-selling is prohibited. We assume that the insurer purchases per-claim reinsurance to transfer its risk exposure to a reinsurer whose premium is computed according to the mean–variance premium principle. Using the stochastic control approach based on the Hamilton–Jacobi–Bellman equation, we derive robust optimal investment–reinsurance strategies and the corresponding value functions. We conclude that the behavior of borrowing typically occurs with a lower wealth level. Finally, numerical examples are given to illustrate our results.

Keywords

Investmentmean-variance premiumreinsurancerobust

MSC classification

Primary: 62P05: Applications to actuarial sciences and financial mathematics
Secondary: 90C39: Dynamic programming 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems) 93E20: Optimal stochastic control
Type
Original Article
Information
Journal of Applied Probability , Volume 62 , Issue 2 , June 2025 , pp. 652 - 673
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust

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