Linear Quadratic Control Techniques Research Articles

Mean-Variance Portfolio Selection in Contagious Markets

We consider a mean-variance portfolio selection problem in a financial market with contagion risk. The risky assets follow a jump-diffusion model, in which jumps are driven by a multivariate Hawkes process with mutual-excitation effect. The mutual-excitation feature of the Hawkes process captures the contagion risk in the sense that each price jump of an asset increases the likelihood of future jumps not only in the same asset but also in other assets. We apply the stochastic maximum principle, backward stochastic differential equation theory, and linear-quadratic control technique to solve the problem and obtain the efficient strategy and efficient frontier in semi-closed form, subject to a non-local partial differential equation. Numerical examples are provided to illustrate our results.

Connections between control allocation and linear quadratic control for weakly redundant systems

In this paper, connections between the control allocation and linear quadratic (LQ) control frameworks for optimally distributing control inputs in weakly input redundant systems are explored. It is also shown that, for a representative class of exogenous disturbance and reference signals, the LQ control technique is identical to the so-called optimal control subspace-based (OCS) control allocation technique. However, for this equivalence to hold, the OCS control allocation technique requires evaluation of a (generally) non-causal relationship between control inputs, while the LQ control technique requires perfect knowledge of the system, disturbance and reference states. In practice, neither of these conditions is achievable; therefore, approximations are needed. In this regard, the OCS control allocation technique is superior because it is explicit about the relationship that must be accurately approximated to attain optimality; this enables good approximations of the optimal relationship to be realized. Conversely, the LQ control technique implicitly approximates the optimal relationship via estimation of states, disturbances and/or reference signals. In a comparison with a classical example based on the Kalman filter, the OCS control allocation is shown to be superior in preserving the optimal alignment of redundant control inputs, thus introducing enhanced performance with reduced cost.

Optimal Asset-Liability Management for an Insurer Under Markov Regime Switching Jump-Diffusion Market

This paper considers an asset-liability management problem under a continuous time Markov regime-switching jump-diffusion market. We assume that the risky stock’s price is governed by a Markov regime-switching jump-diffusion process and the insurance claims follow a Markov regime-switching compound poisson process. Using the Markowitz mean-variance criterion, the objective is to minimize the variance of the insurer’s terminal wealth, given an expected terminal wealth. We get the optimal investment policy. At the same time, we also derive the mean-variance efficient frontier by using the Lagrange multiplier method and stochastic linear-quadratic control technique.

Continuous-Time Mean-Variance Portfolio Selection with Inflation in an Incomplete Market

This paper concerns a continuous-time portfolio selection problem with inflation in an incomplete market. By using the approach of more general stochastic linear quadratic control technique (SLQ), we obtain the optimal strategy and efficient frontier to this problem. Furthermore, a numerical example is also provided.

A class of continuous-time portfolio selection with liability under jump-diffusion processes

A continuous-time mean-variance portfolio selection model is formulated with multiple risky assets and one liability under discontinuous prices which follow jump-diffusion processes in an incomplete market. The correlations between the risky assets and the liability are considered. The corresponding Hamilton–Jacobi–Bellman equation of the problem is presented. The optimal dynamic strategy and the efficient frontier in closed forms are derived explicitly by using stochastic linear-quadratic control technique. Finally, the effects on efficient frontier under the value-at-risk constraint are illustrated.

Continuous-time mean–variance portfolio selection with liability and regime switching

A continuous-time mean–variance model for individual investors with stochastic liability in a Markovian regime switching financial market, is investigated as a generalization of the model of Zhou and Yin [Zhou, X.Y., Yin, G., 2003. Markowitz’s mean–variance portfolio selection with regime switching: A continuous-time model, SIAM J. Control Optim. 42 (4), 1466–1482]. We assume that the risky stock’s price is governed by a Markovian regime-switching geometric Brownian motion, and the liability follows a Markovian regime-switching Brownian motion with drift, respectively. The evolution of appreciation rates, volatility rates and the interest rates are modulated by the Markov chain, and the Markov switching diffusion is assumed to be independent of the underlying Brownian motion. The correlation between the risky asset and the liability is considered. The objective is to minimize the risk (measured by variance) of the terminal wealth subject to a given expected terminal wealth level. Using the Lagrange multiplier technique and the linear-quadratic control technique, we get the expressions of the optimal portfolio and the mean–variance efficient frontier in closed forms. Further, the results of our special case without liability is consistent with those results of Zhou and Yin [Zhou, X.Y., Yin, G., 2003. Markowitz’s mean–variance portfolio selection with regime switching: A continuous-time model, SIAM J. Control Optim. 42 (4), 1466–1482].

On weak spreadability of distributed-parameter systems and its achievement via linear-quadratic control techniques

On weak spreadability of distributed-parameter systems and its achievement via linear-quadratic control techniques

On weak spreadability of distributed-parameter systems and its achievement via linear—quadratic control techniques

On weak spreadability of distributed-parameter systems and its achievement via linear—quadratic control techniques