Optimal control of a big financial company with debt liability under bankrupt probability constraints

TL;DR

This paper develops an optimal control framework for a large financial firm managing dividend payouts and business policies, ensuring bankruptcy probability constraints are met, using stochastic analysis, PDEs, and variational inequalities.

Contribution

It introduces a novel stochastic control model incorporating bankruptcy probability constraints and provides a risk-based capital standard with economic interpretation.

Findings

Derived the optimal control policy under bankruptcy probability constraints.

Established a risk-based capital standard through numerical analysis.

Provided economic insights into the optimal dividend and business strategies.

Abstract

This paper considers an optimal control of a big financial company with debt liability under bankrupt probability constraints. The company, which faces constant liability payments and has choices to choose various production/business policies from an available set of control policies with different expected profits and risks, controls the business policy and dividend payout process to maximize the expected present value of the dividends until the time of bankruptcy. However, if the dividend payout barrier is too low to be acceptable, it may result in the company's bankruptcy soon. In order to protect the shareholders' profits, the managements of the company impose a reasonable and normal constraint on their dividend strategy, that is, the bankrupt probability associated with the optimal dividend payout barrier should be smaller than a given risk level within a fixed time horizon. This paper aims at working out the optimal control policy as well as optimal return function for the company under bankrupt probability constraint by stochastic analysis, PDE methods and variational inequality approach. Moreover, we establish a risk-based capital standard to ensure the capital requirement of can cover the total given risk by numerical analysis and give reasonable economic interpretation for the results.