Mean-variance Asset-liability Management Research Articles

Stochastic control for multiperiod mean-variance asset-liability management

Stochastic control for multiperiod mean-variance asset-liability management

Macroeconomic Volatility in Emerging Countries: A Mean-Variance Asset-Liability Management Model

This paper studies a novel approach for managing macroeconomic volatility in commodity exporting countries. As part of this study, we develop a sovereign risk management model in the context of an Asset-Liability Management (ALM) framework. Our first contribution is an extension of the parsimonious Nijman and Swinkels (2008) pension fund model to a much broader macroeconomic setting using new data while developing unconditional investment allocation and optimal sovereign hedging policies for exporting countries. As the strategies are designed in the static mean-variance setting, the optimal solutions are contingent upon discrete-time realisations of deterministic return moments. However, preliminary investigation of the distributional properties of the data lend credence to the consensus view that the time-invariance assumption may be notoriously incorrect, warranting a relaxation of the restrictive assumptions and the application of advanced statistical procedures. Consequently, as a second contribution, we account for partial autocorrelation, significant heteroskedasticity, cointegration and non-linear dependence in the sample data by adopting GARCH and Error Correction models to enhance the forecasting accuracy of optimal hedge ratios. Thirdly, we propose overlay hedging strategies that, when used in conjunction with the portfolio results, guarantee Pareto efficient allocation. Furthermore, we document substantial increases in Sharpe ratios and significant reduction in Cornish-Fisher value-at-risk and maximum drawdowns. Our portfolio allocation and hedging results suggest buying commodity-linked instruments where the current sovereign market exposure in an endowment is lower than the model implied optimal quantity and selling the instruments where the actual quantity exported exceeds the optimal threshold.

A Random Parameter Model for Continuous-Time Mean-Variance Asset-Liability Management

We consider a continuous-time mean-variance asset-liability management problem in a market with random market parameters; that is, interest rate, appreciation rates, and volatility rates are considered to be stochastic processes. By using the theories of stochastic linear-quadratic (LQ) optimal control and backward stochastic differential equations (BSDEs), we tackle this problem and derive optimal investment strategies as well as the mean-variance efficient frontier analytically in terms of the solution of BSDEs. We find that the efficient frontier is still a parabola in a market with random parameters. Comparing with the existing results, we also find that the liability does not affect the feasibility of the mean-variance portfolio selection problem. However, in an incomplete market with random parameters, the liability can not be fully hedged.

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.

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.

Markowitz’s mean–variance asset–liability management with regime switching: A time-consistent approach

In this article, we provide the first study in the time consistent solution of the mean–variance asset–liability management (MVALM). The framework is even considered under a continuous time Markov regime-switching setting. Using the extended Hamilton–Jacobi–Bellman equation (HJB) (see Björk and Murgoci (2010)), we show that the time consistent equilibrium control is state dependent in the sense that it depends on the uncontrollable liability process, which is in substantial contrast with the time consistent solution of the similar problem in Björk and Murgoci (2010), in which it is independent of the state. Finally, we give a numerical comparison between our work with the corrected version (as obtained here) of pre-commitment strategy in Chen et al. (2008).

Multi-period mean–variance asset–liability management with uncontrolled cash flow and uncertain time-horizon

This paper considers an asset–liability management problem under a multi-period mean–variance model with uncontrolled cash flow and uncertain time-horizon. The difference from the existing literature is that the liability is assumed to be influenced not only by the stochastic return of the liability but also by some uncontrolled cash flows, which can be explained as, for example, stochastic expenditure of individual investors, or claim processes of insurers. Firstly, the original problem is translated into a standard multi-period stochastic optimal control problem by introducing a Lagrange multiplier, and the corresponding analytical solution is derived by adopting the dynamic programming approach. Secondly, according to Lagrange duality theorem, closed-form expressions for the efficient investment strategy and the mean–variance efficient frontier are obtained. Moreover, a multi-period version of two-fund separation theorem is proved, and some special cases are discussed. Finally, some numerical examples are presented to illustrate our results.

Continuous-time mean–variance asset–liability management with endogenous liabilities

This paper investigates a continuous-time mean–variance asset–liability management problem with endogenous liabilities in a more general market where all the assets can be risky. Different from exogenous liabilities that cannot be controlled, the endogenous liabilities can be controlled by various financial instruments and investors’ decisions. For example, a company can raise fund by issuing different kinds of bonds. Types and quantities of the bonds are controlled by the company itself. Investors optimize allocation not only for their assets, but also for their liabilities under our model. This makes the analysis of the problem more challenging than in the setting based on exogenous liabilities. In this paper, we first prove the existence and uniqueness of the solution to the associated Riccati-type equation by using the Khatri–Rao product technique and the relevant stochastic control theory; we then derive closed form expressions of the efficient strategy and the mean–variance efficient frontier by using the Lagrange multiplier method and the Hamilton–Jacobi–Bellman equation approach, and we next discuss two degenerated cases; finally, we present some numerical examples to illustrate the results obtained in this paper.

Mean–variance asset–liability management: Cointegrated assets and insurance liability

The cointegration of major financial markets around the globe is well evidenced with strong empirical support. This paper considers the continuous-time mean–variance (MV) asset–liability management (ALM) problem for an insurer investing in an incomplete financial market with cointegrated assets. The number of trading assets is allowed to be less than the number of Brownian motions spanning the market. The insurer also faces the risk of paying uncertain insurance claims during the investment period. We assume that the cointegration market follows the diffusion limit of the error-correction model for cointegrated time series. Using the Markowitz (1952) MV portfolio criterion, we consider the insurer’s problem of minimizing variance in the terminal wealth, given an expected terminal wealth subject to interim random liability payments following a compound Poisson process. We generalize the technique developed by Lim (2005) to tackle this problem. The particular structure of cointegration enables us to solve the ALM problem completely in the sense that the solutions of the continuous-time portfolio policy and efficient frontier are obtained as explicit and closed-form formulas.

Markowitz's Mean-Variance Asset–Liability Management with Regime Switching: A Multi-Period Model

This paper considers an optimal portfolio selection problem under Markowitz's mean-variance portfolio selection problem in a multi-period regime-switching model. We assume that there are n + 1 securities in the market. Given an economic state which is modelled by a finite state Markov chain, the return of each security at a fixed time point is a random variable. The return random variables may be different if the economic state is changed even for the same security at the same time point. We start our analysis from the no-liability case, in the spirit of Li and Ng (2000), both the optimal investment strategy and the efficient frontier are derived. Then we add uncontrollable liability into the model. By direct comparison with the no-liability case, the optimal strategy can be derived explicitly.

Conditions for Positive and Nonnegative Definiteness in Terms of Pseudoinverses

Matrix pseudoinverses producing necessary and sufficient conditions for positive and nonnegative definiteness