Article, 2023

Robust optimal asset-liability management with mispricing and stochastic factor market dynamics

Insurance Mathematics and Economics, ISSN 1873-5959, 0167-6687, Volume 113, Pages 251-273, 10.1016/j.insmatheco.2023.09.001

Contributors

Wang, Ning 0000-0002-7667-2423 [1] Zhang, Yumo 0000-0003-0915-5116 (Corresponding author) [2]

Affiliations

  1. [1] Macquarie University
    2. [NORA names: Australia; Oceania; OECD];
  2. [2] University of Copenhagen
    3. [NORA names: KU University of Copenhagen; University; Denmark; Europe, EU; Nordic; OECD]

Abstract

This paper investigates a robust optimal asset-liability management problem under an expected utility maximization criterion. More specifically, the manager is concerned about the potential model uncertainty and aims to seek the robust optimal investment strategies. We incorporate an uncontrollable random liability described by a generalized drifted Brownian motion. Also, the manager has access to an incomplete financial market consisting of a risk-free asset, a market index with potentially path-dependent, time-varying risk premium and volatility, and a pair of mispriced stocks. The market dynamics are assumed to rely on an affine-form, square-root factor process and the price error is modeled by a co-integrated system. We adopt a backward stochastic differential equation approach hinging on the martingale optimality principle to solve this non-Markovian robust control problem. Closed-form expressions for the robust optimal investment strategies, the probability perturbation process under the well-defined worst-case scenario and the corresponding value function are derived. The admissibility of the robust optimal controls is verified under some technical conditions. Finally, we perform some numerical examples to illustrate the effects of model parameters on the robust investment strategies and draw some economic interpretations from these results.

Keywords

Brownian motion, admission, affine-form, asset-liability management, asset-liability management problem, assets, closed-form expressions, co-integrated system, conditions, control, control problem, corresponding value function, criteria, drift Brownian motion, dynamics, economic interpretation, effect, effects of model parameters, error, examples, expression, factorization process, financial markets, function, hinge, incomplete financial markets, index, interpretation, investment strategies, liability, management, management problems, market, market dynamics, market index, martingale, martingale optimality principle, maximization, maximization criterion, mispriced stocks, mispricing, model parameters, model uncertainty, motion, numerical examples, optimal asset-liability management, optimal control, optimal investment strategy, optimization principle, pair of mispriced stocks, pairs, parameters, path dependence, perturbation process, potential model uncertainty, premium, price, pricing errors, principles, probability, problem, process, random liabilities, results, risk premium, robust control problem, robust investment strategy, robust optimal control, robust optimal investment strategy, stock, strategies, system, technical condition, time-varying risk premium, uncertainty, value function, volatility

Funders

  • National Natural Science Foundation of China

Data Provider: Digital Science

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