Abstract
How do investors require a distribution of the wealth among multiple risky assets while facing the risk of the uncontrollable payment for random liabilities? To cope with this problem, firstly, this paper explores the approach of asset-liability management under the state-dependent risk aversion with only risky assets, which has been considered under a continuous-time Markov regime-switching setting. Next, based on this realistic modelling, an extended Hamilton-Jacob-Bellman (HJB) system has been necessarily established for solving the optimization problem of asset-liability management. It has been derived closed-form analytical expressions applied in the time-inconsistent investment with optimal control theory to see that happens to the optimal value of the function. Ultimately, numerical examples presented with comparisons of the analytical results under different market conditions are exposed to analyse numerically the developed mean variance asset liability management strategy. We find that our proposed model can explain the financial phenomena more effectively and accurately.
Highlights
IntroductionWell known as an essential topic in financial markets, has been done in deep researches by many scholars after the first reported by Markowitz [1]
Portfolio optimization selection problem, well known as an essential topic in financial markets, has been done in deep researches by many scholars after the first reported by Markowitz [1]
Previous researches in this area are classified for the endogenous habit formation [2], the classic constant relative risk aversion (CRRA) by Yu and Yuan [4], the hyperbolic discounting [3], and the utilities like the mean-variance utility proposed by Li et al [5]
Summary
Well known as an essential topic in financial markets, has been done in deep researches by many scholars after the first reported by Markowitz [1]. In recent paper by Li et al [6], the analytical solution portfolio optimization problem involving stochastic shortterm interest rates is provided, which can be controlled by the mean-variance utility function with state dependent risk aversion (SDRA). On the basis of the work of Björk et al [3], it is determinate to make a further realistic financial model, and it makes sense to select a regime-switching market with only risky assets. The rest of the paper is completed as follows: the setting of the financial market will be explained, with the developed structure of mean-variance asset-liability management with state-dependent risk aversion in a regime-switching market with only risky assets.
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