Optimal Asset-liability Management Research Articles

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

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.

Robust optimal asset-liability management under square-root factor processes and model ambiguity: a BSDE approach

This article studies robust optimal asset-liability management problems for an ambiguity-averse manager in a possibly non-Markovian environment with stochastic investment opportunities. The manager has access to one risk-free asset and one risky asset in a financial market. The market price of risk relies on a stochastic factor process satisfying an affine-form, square-root, Markovian model, whereas the risky asset’s return rate and volatility are potentially given by general non-Markovian, unbounded stochastic processes. This financial framework includes, but is not limited to, the constant elasticity of variance (CEV) model, the family of 4/2 stochastic volatility models, and some path-dependent non-Markovian models, as exceptional cases. As opposed to most of the papers using the Hamilton-Jacobi-Bellman-Issacs (HJBI) equation to deal with model ambiguity in the Markovian cases, we address the non-Markovian case by proposing a backward stochastic differential equation (BSDE) approach. By solving the associated BSDEs explicitly, we derive, in closed form, the robust optimal controls and robust optimal value functions for power and exponential utility, respectively. In addition, analytical solutions to some particular cases of our model are provided. Finally, the effects of model ambiguity and market parameters on the robust optimal investment strategies are illustrated under the CEV model and 4/2 model with numerical examples.

Optimal investment strategies for asset-liability management with affine diffusion factor processes and HARA preferences

<p style='text-indent:20px;'>This paper investigates an optimal asset-liability management problem within the expected utility maximization framework. The general hyperbolic absolute risk aversion (HARA) utility is adopted to describe the risk preference of the asset-liability manager. The financial market comprises a risk-free asset and a risky asset. The market price of risk depends on an affine diffusion factor process, which includes, but is not limited to, the constant elasticity of variance (CEV), Stein-Stein, Schöbel and Zhu, Heston, 3/2, 4/2 models, and some non-Markovian models, as exceptional examples. The accumulative liability process is featured by a generalized drifted Brownian motion with possibly unbounded and non-Markovian drift and diffusion coefficients. Due to the sophisticated structure of HARA utility and the non-Markovian framework of the incomplete financial market, a backward stochastic differential equation (BSDE) approach is adopted. By solving a recursively coupled BSDE system, closed-form expressions for both the optimal investment strategy and optimal value function are derived. Moreover, explicit solutions to some particular cases of our model are provided. Finally, numerical examples are presented to illustrate the effect of model parameters on the optimal investment strategies in several particular cases.</p>

Asset-liability management with state-dependent utility in the regime-switching market

This paper considers a state-dependent optimal asset-liability management problem in continuous-time settings. The investor maximizes the expected state-dependent utility of the terminal asset-liability ratio in a regime-switching market to better describe insurance companies’ needs for asset-liability matching and regulation with background risk. We apply the stochastic dynamic programming method to get closed-form results. We find that the optimal strategy in the state-dependent utility case is the same, and the optimal value function differs from the state-independent utility case. Finally, we study how the parameters impact the optimal investment strategy and corresponding value functions through numerical examples.

Robust optimal asset–liability management with delay and ambiguity aversion in a jump-diffusion market

In this paper, we consider a robust optimal asset–liability management problem with delay for an ambiguity-averse investor (AAI), who does not hold a firm belief towards not only the drift parameters but also the jump intensity in the wealth process. The objective of AAI is to maximise the robust value involving the expected utility of a weighted sum of terminal wealth and a penalisation of model uncertainty. In addition, the wealth process is modelled by a stochastic delay equation with jump via introducing the performance-related capital inflow/outflow. Applying the technique of robust optimal theory and Hamilton–Jacobi–Bellman equation, we derive the optimal results and the proof of verification theorem for the general utility functions and liability processes. In the case of the exponential utility function and a positive liability process, we prove the existence and uniqueness of the robust optimal investment strategy and find it naturally satisfies the constraint of no-short selling. Meanwhile, we adopt a special method to solve the corresponding Riccati equation and obtain the value function in explicit form. Furthermore, the results under the complete memory are discussed in detail. Finally, some numerical examples are provided to illustrate the influence of model parameters on the optimal strategy as well as the economic interpretation behind it.

Robust optimal asset-liability management with penalization on ambiguity

<p style='text-indent:20px;'>In this paper, we study the robust optimal asset- problems for an ambiguity-averse investor, who does not have perfect information in the drift terms of the risky asset and liability processes. Two different kinds of objectives are considered: <inline-formula><tex-math id="M1">\begin{document}$ (i) $\end{document}</tex-math></inline-formula> Maximizing the minimal expected utility of the terminal wealth; <inline-formula><tex-math id="M2">\begin{document}$ (ii) $\end{document}</tex-math></inline-formula> Minimizing the maximal cumulative deviation. The ambiguity in both problems is described by a set of equivalent measures to the reference model. By the stochastic dynamic programming approach and Hamilton-Jacobi-Bellman (HJB) equation, we derive closed-form expressions for the value function and corresponding robust optimal investment strategy in each problem. Furthermore, some special cases are provided to investigate the effect of model uncertainty on the optimal investment strategy. Finally, the economic implication and parameter sensitivity are analyzed by some numerical examples. We also compare the robust optimal investment strategies in two different problems.</p>

Robust Optimal Asset-Liability Management Under Square-Root Factor Processes and Model Ambiguity: A BSDE Approach

Robust Optimal Asset-Liability Management Under Square-Root Factor Processes and Model Ambiguity: A BSDE Approach

Insurer Optimal Asset Allocation in a Small and Closed Economy: The Case of Iran’s Social Security Organization

We seek to determine the optimal amount of the insurer’s investment in all types of assets for a small and closed economy. The goal is to detect the implications and contributions the risk seeker and risk aversion insurer commonly make and the effectiveness in the investment decision. Also, finding the optimum portfolio for each is the main goal of the present study. To this end, we adopted the optimal asset-liability management (ALM) method to control the firm's risk of financial stability and growth by balancing the assets and liabilities of the firm. In the process, stochastic interest rates and inflation risks were taken into account according to the expected utility maximization framework. All assets were established and calculated by the Kalman Filter with the stochastic interest rate following the Hull-White model; an additional stochastic process models the inflation risk. To consider the stochastic process, we employed the geometric Brownian motion in the liability process to ensure a definite liability value. We chose Iran’s Social Security Organization as our sample insurer company since it has a portfolio of five types of assets and four types of liabilities, and operates in a small and closed economy. By Applying the ALM method with the stochastic control theory approach, we acquire the optimal investment strategies for insurers to minimize their risk. Our findings demonstrate the effects of model parameters, such as the degree of risk-taking on the insurer decision.

Optimal risk sharing in insurance networks

We discuss the impact of risk sharing and asset–liability management on capital requirements. Our analysis contributes to the evaluation of the merits and deficiencies of different risk measures. In particular, we highlight that the class of V@R-based risk measures allows for a substantial reduction of the total capital requirement in corporate networks that share risks between entities. We provide case studies that complement previous theoretical results and demonstrate their practical relevance. For large networks, optimal asset–liability management is often contrary to those strategies that are desirable from a regulatory point of view.

Mean-variance asset-liability management with affine diffusion factor process and a reinsurance option

ABSTRACTThis paper considers an optimal asset-liability management (ALM) problem for an insurer under the mean-variance criterion. It is assumed that the value of liabilities is described by a geometric Brownian motion (GBM). The insurer's surplus process is modeled by a general jump process generated by a marked point process. The financial market consists of one risk-free asset and n risky assets with the risk premium relying on an affine diffusion factor process. By transferring a proportion of insurance risk to a reinsurer and investing the surplus into the financial market, the insurer aims to maximize the expected terminal net wealth and, at the same time, minimize the corresponding variance of the terminal net wealth. By using a backward stochastic differential equation (BSDE) approach, closed-form expressions for both the efficient strategy and efficient frontier are derived. To illustrate the main results, we study an example with the Heston stochastic volatility (SV) model and numerically analyze the economic behavior of the efficient frontier. Finally, a generalization of the Mutual Fund Theorem is obtained.

Optimal dynamic asset-liability management with stochastic interest rates and inflation risks

This paper considers an optimal asset-liability management problem with stochastic interest rates and inflation risks under the expected utility maximization framework, where the stochastic interest rate follows the Hull-White interest rate model and the inflation risk is modelled by an additional stochastic process. The investor can invest in n+1 assets: cash, a default-free zero-coupon bond, an inflation-indexed bond and n−2 stocks. The liability process is given by a geometric Brownian motion rather than a Brownian motion to ensure a definite liability value. Applying the stochastic control theory and partial differential equation approach, we obtain the explicit solutions of optimal investment strategies for the power utility and exponential utility functions. We also provide numerical examples to show the effects of model parameters on the optimal investment strategies.

Optimal mean–variance asset-liability management with stochastic interest rates and inflation risks

This paper considers an optimal asset-liability management problem with stochastic interest rates and inflation risks under the mean–variance framework. It is assumed that there are $$n+1$$ assets available in the financial market, including a risk-free asset, a default-free zero-coupon bond, an inflation-indexed bond and $$n-2$$ risky assets (stocks). Moreover, the liability of the investor is assumed to follow a geometric Brownian motion process. By using the stochastic dynamic programming principle and Hamilton–Jacobi–Bellman equation approach, we derive the efficient investment strategy and efficient frontier explicitly. Finally, we provide numerical examples to illustrate the effects of model parameters on the efficient investment strategy and efficient frontier.

Optimal asset–liability management with liquidity constraints and stochastic interest rates in the expected utility framework

This paper studies the optimal investment problem for an investor who wants to maximize the expected utility of the terminal asset–liability ratio under liquidity constraints and stochastic interest rates. By using the method of stochastic control and variable change techniques, we derive the closed-form solutions of optimal investment strategies and optimal terminal asset–liability ratios for the constant relative risk averse (CRRA) utility and constant absolute risk averse (CARA) utility functions. Moreover, a new verification theorem without the usual Lipschitz assumption is proved. Finally, we provide numerical examples to illustrate how liquidity constraints and stochastic interest rates affect the optimal investment strategies and optimal terminal asset–liability ratios.

Mean–variance asset–liability management with asset correlation risk and insurance liabilities

Consider an insurer who invests in the financial market where correlations among risky asset returns are randomly changing over time. The insurer who faces the risk of paying stochastic insurance claims needs to manage her asset and liability by taking into account of the correlation risk. This paper investigates the impact of correlation risk to the optimal asset–liability management (ALM) of an insurer. We employ the Wishart process to model the stochastic covariance matrix of risky asset returns. The insurer aims to minimize the variance of the terminal wealth given an expected terminal wealth subject to the risk of paying out random liabilities of compound Poisson process. This ALM problem then becomes a linear–quadratic stochastic optimal control problem with stochastic volatilities, stochastic correlations and jumps. The recognition of an affine form in the solution process enables us to derive the explicit closed-form solution to the optimal ALM portfolio policy, obtain the efficient frontier, and identify the condition that the solution is well behaved.

Applying stochastic programming to insurance portfolios stress-testing

The introduction of the Solvency II regulatory framework in 2011 and unprecendented property and casualty (P/C) claims experienced in recent years by large insurance firms have motivated the adoption of risk-based capital allocation policies in the insurance sector. In this article, we present the key features of a dynamic stochastic program leading to an optimal asset-liability management and capital allocation strategy by a large P/C insurance company and describe how from such formulation a specific, industry-relevant, stress-testing analysis can be derived. Throughout the article the investment manager of the insurance portfolio is regarded as the relevant decision-maker: he faces exogenous constraints determined by the core insurance division and is subject to the capital allocation policy decided by the management, consistently with the company's risk exposure. A novel approach to stress-testing analysis by the insurance management, based on a recursive solution of a large-scale dynamic stochastic p...

Continuous-Time Mean-Variance Asset-Liability Management with Hidden Markovian Regime Switching

This paper considers a continuous-time mean-variance asset-liability management problem with incompletely observable information. An investor can only observe the prices of the asset and liability and the dynamics of the unobservable states of the underlying financial market is described by a hidden Markovian chain. The price of the risky asset is assumed to be governed by a hidden Markovian regime switching geometric Brownian motion and the liability is assumed to follow a hidden Markovian regime switching Brownian motion with drift, respectively. The appreciation rates of the risky asset and the liability are modulated by the hidden Markovian chain. By using the separation principle, the filtering-estimation problem and the mean-variance asset-liability management problem are discussed. The explicit expressions for the optimal asset-liability management strategy and the mean-variance efficient frontier are determined by using the stochastic maximum principle.

Spectral decomposition of optimal asset–liability management

This paper concerns optimal asset–liability management when the assets and the liabilities are modeled by means of correlated geometric Brownian motions as suggested in Gerber and Shiu [2003. Geometric Brownian motion models for assets and liabilities: from pension funding to optimal dividends. North American Actuarial Journal 7(3), 37–51]. In a first part, we apply singular stochastic control techniques to derive a free boundary equation for the optimal value creation as a growth of liabilities or as dividend payment to shareholders. We provide analytical solutions to the Hamilton–Jacobi–Bellman (HJB) optimality equation in a rather general context. In a second part, we study the convergence of the cash flows to the optimal value creation using spectral methods. For particular cases, we also provide a series expansion for the probabilities of bankruptcy in finite time.

Optimal asset–liability management with constraints: A dynamic programming approach

This paper is devoted to the analysis of a discrete-time dynamic programming algorithm for the numerical solution of an optimal asset-liability management model with transaction costs and in presence of constraints. By exploiting the financial properties of the model, we propose an approximation method based on the classical dynamic programming algorithm, which reduces significantly the computational and storage requirements of the algorithm and avoids any artificial boundary condition. The regularity of the value function is used to estimate the global error introduced by the numerical procedure and to prove a convergence result.

A MODEL FOR THE OPTIMAL ASSET-LIABILITY MANAGEMENT FOR INSURANCE COMPANIES

This paper is devoted to the formulation of a model for the optimal asset-liability management for insurance companies. We focus on a typical guaranteed investment contract, by which the holder has the right to receive after T years a return that cannot be lower than a minimum predefined rate rg. We take account of the rules that usually are imposed to insurance companies in the management of this funds as reserves and solvency margin. We formulate the problem as a stochastic optimization problem in a discrete time setting comparing this approach with the so-called hedging approach. The utility function to maximize depends on various parameters including specific goals of the company management. Some preliminary numerical results are reported to ease the comparison between the two approaches.