Optimal Asset Allocation Problem Research Articles

Dual control Monte-Carlo method for tight bounds of value function in regime switching utility maximization

In this paper, we study the dual control approach for the optimal asset allocation problem in a continuous-time regime-switching market. We find the lower and upper bounds of the value function that is a solution to a system of fully coupled nonlinear partial differential equations. These bounds can be tightened with additional controls to the dual process. We suggest a Monte-Carlo algorithm for computing the tight lower and upper bounds and show the method is effective with a variety of utility functions, including power, non-HARA and Yaari utilities. The latter two utilities are beyond the scope of any current methods available in finding the value function.

Large‐Scale Portfolio Optimization Using Multiobjective Evolutionary Algorithms and Preselection Methods

Portfolio optimization problems involve selection of different assets to invest in order to maximize the overall return and minimize the overall risk simultaneously. The complexity of the optimal asset allocation problem increases with an increase in the number of assets available to select from for investing. The optimization problem becomes computationally challenging when there are more than a few hundreds of assets to select from. To reduce the complexity of large‐scale portfolio optimization, two asset preselection procedures that consider return and risk of individual asset and pairwise correlation to remove assets that may not potentially be selected into any portfolio are proposed in this paper. With these asset preselection methods, the number of assets considered to be included in a portfolio can be increased to thousands. To test the effectiveness of the proposed methods, a Normalized Multiobjective Evolutionary Algorithm based on Decomposition (NMOEA/D) algorithm and several other commonly used multiobjective evolutionary algorithms are applied and compared. Six experiments with different settings are carried out. The experimental results show that with the proposed methods the simulation time is reduced while return‐risk trade‐off performances are significantly improved. Meanwhile, the NMOEA/D is able to outperform other compared algorithms on all experiments according to the comparative analysis.

Managing ambiguity in asset allocation

This paper is about the issue of input parameter uncertainty in portfolio optimization in a discrete setting with finite states (such as the case in a world with different macroeconomic regimes). In such a setting, being unable to assign reliable point estimates to the probabilities (or frequencies) of the states creates the ambiguity. We first describe how this ambiguity can be modeled probabilistically. Then, we show how this added uncertainty can be dealt with in optimal asset allocation problems. In simple-yet-realistic example applications we demonstrate that without sacrificing much of the upside, ambiguity managed portfolios may enhance the uniformity of returns across different states when compared to portfolios constructed by traditional methods. We stress that a key conclusion to be taken from these methods builds the case for insurance-like and potentially negative-yielding investments such as bonds and commodities so as to hedge the unforeseeable macrouncertainties for a smoother portfolio performance. Finally, we offer a variety of problem domains in which ambiguity management can be nested including macroeconomic scenario-based asset allocation, investing with regime-switching models, momentum investing, and risk-based investing.

Intuitive Ambiguity Management

This paper is about the issue of input parameter uncertainty in portfolio optimization in a discrete setting with finite states (such as the case in a world with different macroeconomic regimes). In such a setting, being unable to assign reliable point estimates to the probabilities (or frequencies) of the states creates the ambiguity. We first describe how this ambiguity can be modeled probabilistically. Then, we show how this added uncertainty can be dealt with in optimal asset allocation problems. In simple-yet-realistic example applications we demonstrate that without sacrificing much of the upside, ambiguity managed portfolios enhance the uniformity of returns across different states when compared to portfolios constructed by traditional methods. We stress that a key advice from these methods builds the case for insurance-like and potentially negative yielding investments such as bonds and commodities so as to hedge the unforeseeable macro uncertainties for a smoother portfolio performance. Finally, we offer a variety of problem domains in which ambiguity management can be nested including macroeconomic scenario based asset allocation, investing with regime switching models, momentum investing, and risk-based investing.

A Stochastic Flows Approach for Asset Allocation with Hidden Economic Environment

An optimal asset allocation problem for a quite general class of utility functions is discussed in a simple two-state Markovian regime-switching model, where the appreciation rate of a risky share changes over time according to the state of a hidden economy. As usual, standard filtering theory is used to transform a financial model with hidden information into one with complete information, where a martingale approach is applied to discuss the optimal asset allocation problem. Using a martingale representation coupled with stochastic flows of diffeomorphisms for the filtering equation, the integrand in the martingale representation is identified which gives rise to an optimal portfolio strategy under some differentiability conditions.

Optimal Investment with Time-Varying Stochastic Endowments

This paper considers a utility maximization and optimal asset allocation problem in the presence of a stochastic endowment that cannot be fully hedged through trading in the financial market. We rely on the dynamic programming approach to solve the optimization problem. The properties of the value function, particularly the homogeneity, are used to reduce the HJB equation by one dimension. Furthermore, the optimal strategy is derived, and its asymptotic behavior is discussed.

Optimal currency carry trade strategies

This paper studies the optimal asset allocation problem of an investor with a portfolio given by the U.S. risk-free asset and a carry trade benchmark comprising the currencies of the G10 countries. Our optimal strategy is able to adapt to macroeconomic conditions and avoid the so-called crash risk inherent in standard carry trade strategies by constructing a vector of dynamic weights that depends on a set of state variables. We find that the U.S. Ted spread, the U.S. average forward discount, the CRB Industrial return, and a global monetary policy indicator are the key drivers of optimal currency carry trade strategies.

Portfolio optimization in a regime-switching market with derivatives

We consider the optimal asset allocation problem in a continuous-time regime-switching market. The problem is to maximize the expected utility of the terminal wealth of a portfolio that contains an option, an underlying stock and a risk-free bond. The difficulty that arises in our setting is finding a way to represent the return of the option by the returns of the stock and the risk-free bond in an incomplete regime-switching market. To overcome this difficulty, we introduce a functional operator to generate a sequence of value functions, and then show that the optimal value function is the limit of this sequence. The explicit form of each function in the sequence can be obtained by solving an auxiliary portfolio optimization problem in a single-regime market. And then the original optimal value function can be approximated by taking the limit. Additionally, we can also show that the optimal value function is a solution to a dynamic programming equation, which leads to the explicit forms for the optimal value function and the optimal portfolio process. Furthermore, we demonstrate that, as long as the current state of the Markov chain is given, it is still optimal for an investor in a multiple-regime market to simply allocate his/her wealth in the same way as in a single-regime market.

A BSDE approach to risk-based asset allocation of pension funds with regime switching

An asset allocation problem of a member of a defined contribution (DC) pension fund is discussed in a hidden, Markov regime-switching, economy using backward stochastic differential equations, (BSDEs). A risk-based approach is considered, where the member selects an optimal asset mix with a view to minimizing the risk described by a convex risk measure of his/her terminal wealth. Firstly, filtering theory is adopted to transform the hidden, Markov regime-switching, economy into one with complete observations and to develop, (robust), filters for the hidden Markov chain. Then the optimal asset allocation problem of the member is formulated as a two-person, zero-sum stochastic differential game between the member and the market in the economy with complete observations. The BSDE approach is then used to solve the game problem and to characterize the saddle point of the game problem. An explicit expression for the optimal asset mix is obtained in the case of a convex risk measure with quadratic penalty and it can be considered a generalized version of the Merton ratio. An explicit expression for the optimal strategy of the market is also obtained, which leads to a risk-neutral wealth dynamic and may provide some insights into asset pricing in the economy with inflation risk and regime-switching risk. Numerical examples are provided to illustrate financial implications of the BSDE solution.

Asset allocation under stochastic interest rate with regime switching

We investigate an optimal asset allocation problem in a Markovian regime-switching financial market with stochastic interest rate. The market has three investment opportunities, namely, a bank account, a share and a zero-coupon bond, where stochastic movements of the short rate and the share price are governed by a Markovian regime-switching Vasicek model and a Markovian regime-switching Geometric Brownian motion, respectively. We discuss the optimal asset allocation problem using the dynamic programming approach for stochastic optimal control and derive a regime-switching Hamilton–Jacobi–Bellman (HJB) equation. Particular attention is paid to the exponential utility case. Numerical and sensitivity analysis are provided for this case. The numerical results reveal that regime-switches described by a two-state Markov chain have significant impacts on the optimal investment strategies in the share and the bond. Furthermore, the market prices of risk in both the bond and share markets are crucial factors in determining the optimal investment strategies.

Elasticity approach to asset allocation in discrete time

In this paper, we apply the elasticity approach to optimal asset allocation problems in discrete-time setting. In particu- lar, firstly, for a portfolio optimization problem, which targets to maximize the expected utility of the terminal wealth of a portfo- lio of an option, the underlying stock, and the risk-free bond, the elasticity approach can decompose this problem into a reduced optimization problem, consisting of only the stock and bond, and a pure delta neutral hedging problem. This decomposition provides a discrete-time version of the optimal alternative to the delta hedge, which was initially proposed in continuous time. Moreover, the general principle given by the pure delta neutral strategy is analyzed in our setting. Secondly, the same approach is applied to an optimal investment problem with defaultable securities, and show that this problem is essentially the same as the above mentioned reduced optimization problem. This work can be regarded as an extension of the elasticity approach in Kraft (Mathematical Methods of Operations Research 58(1) (2003), 159-182) to discrete-time models, and it shows that this approach can largely deduce the asset allocation problems in complete market.

Asset allocation under threshold autoregressive models

We discuss the asset allocation problem in the important class of parametric non-linear time series models called the threshold autoregressive model in (J. Roy. Statist. Soc. Ser. A 1977; 140:34–35; Patten Recognition and Signal Processing. Sijthoff and Noordhoff: Netherlands, 1978; and J. Roy. Statist. Soc. Ser. B 1980; 42:245–292). We consider two specific forms, one self-exciting (i.e. the SETAR model) and the other smooth (i.e. the STAR) model developed by Chan and Tong (J. Time Ser. Anal. 1986; 7:179–190). The problem of maximizing the expected utility of wealth over a planning horizon is considered using a discrete-time dynamic programming approach. This optimization approach is flexible enough to deal with the optimal asset allocation problem under a general stochastic dynamical system, which includes the SETAR model and the STAR model as particular cases. Numerical studies are conducted to demonstrate the practical implementation of the proposed model. We also investigate the impacts of non-linearity in the SETAR and STAR models on the optimal portfolio strategies. Copyright © 2011 John Wiley & Sons, Ltd.

Filtering of a Multi-Dimension Stochastic Volatility Model

In this article, we study a stochastic volatility model for a class of risky assets. We assume that the volatilities of the assets are driven by a common state of economy, which is unobservable and represented by a hidden Markov chain. Under this hidden Markov model (HMM), we develop recursively computable filtering equations for certain functionals of the chain. Expectation maximization (EM) parameter estimation is then used. Applications to an optimal asset allocation problem with mean-variance utility are given.

On “optimal pension management in a stochastic framework” with exponential utility

This paper reconsiders the optimal asset allocation problem in a stochastic framework for defined-contribution pension plans with exponential utility, which has been investigated by Battocchio and Menoncin [Battocchio, P., Menoncin, F., 2004. Optimal pension management in a stochastic framework. Insurance: Math. Econ. 34, 79–95]. When there are three types of asset, cash, bond and stock, and a non-hedgeable wage risk, the optimal pension portfolio composition is horizon dependent for pension plan members whose terminal utility is an exponential function of real wealth (nominal wealth-to-price index ratio). With market parameters usually assumed, wealth invested in bond and stock increases as retirement approaches, and wealth invested in cash asset decreases. The present study also shows that there are errors in the formulation of the wealth process and control variables in solving the optimization problem in the study of Battocchio and Menoncin, which render their solution erroneous and lead to wrong results in their numerical simulation.

A benchmarking approach to optimal asset allocation for insurers and pension funds

We solve the optimal asset allocation problem for an insurer or pension fund by using a benchmarking approach. Under this approach the objective is an increasing function of the relative performance of the asset portfolio compared to a benchmark. The benchmark can be, for example, a function of an insurer’s liability payments, or the (either contractual or target) payments of a pension fund. The benchmarking approach tolerates but progressively penalizes shortfalls, while at the same time progressively rewards outperformance. Working in a general, possibly non-Markovian setting, a solution to the optimization problem is presented, providing insights into the impact of benchmarking on the resulting optimal portfolio. We further illustrate the results with a detailed example involving an option based benchmark of particular interest to insurers and pension funds, and present closed form solutions.

Numerical solution of the Hamilton–Jacobi–Bellman formulation for continuous time mean variance asset allocation

We solve the optimal asset allocation problem using a mean variance approach. The original mean variance optimization problem can be embedded into a class of auxiliary stochastic linear-quadratic (LQ) problems using the method in Zhou and Li (2000) and Li and Ng (2000). We use a finite difference method with fully implicit timestepping to solve the resulting nonlinear Hamilton–Jacobi–Bellman (HJB) PDE, and present the solutions in terms of an efficient frontier and an optimal asset allocation strategy. The numerical scheme satisfies sufficient conditions to ensure convergence to the viscosity solution of the HJB PDE. We handle various constraints on the optimal policy. Numerical tests indicate that realistic constraints can have a dramatic effect on the optimal policy compared to the unconstrained solution.

A Benchmarking Approach to Optimal Asset Allocation for Insurers and Pension Funds

We solve the optimal asset allocation problem for an insurer or pension fund by using a benchmarking approach. Under this approach the objective is an increasing function of the relative performance of the asset portfolio compared to a benchmark. The benchmark can be, for example, a function of an insurer's liability payments, or the (either contractual or target) payments of a pension fund. The benchmarking approach tolerates but progressively penalizes shortfalls, while at the same time progressively rewarding out-performance. Working in a general, possibly non-Markovian setting, a solution to the optimization problem is presented, providing insights as to the impact of benchmarking on the resulting optimal portfolio.

Optimization-Based Generation Asset Allocation for Forward and Spot Markets

One of the most important daily decisions that a Genco has to make is to allocate generation assets between the forward and spot markets. That is, how much capacity should be contracted in the forward market and how much should be kept to bid in spot market? This paper focuses on generation asset allocation between monthly forward contracts, such as bilateral contracts, futures contracts, options contracts, and daily spot markets, considering operating costs and constraints of generating units, as well as spot price risk. The problem is to find the optimal hedging position based on the known forward price and the forecasted hourly spot prices and is formulated based on the model of PJM market. The double dynamic programming method is applied to solve this optimal asset allocation problem with all the short-term operating constraints of the generating unit satisfied. Three types of forward contracts that are commonly used in practice are considered and their impact on generation asset allocation are analyzed and compared. The analytic relationship between the optimal contract quantity of a particular type and spot generation is established. Based on this relationship, the applicability and characteristics of a particular type of contract are discussed. Furthermore, with the solution to the generation asset allocation problem as a basis, the pricing strategy in the forward market is analyzed. A Nash game model is established and an iterative process is developed to determine the equilibrium pricing of futures contracts. Numerical testing shows that the method for the generation asset allocation is effective. Various factors influencing the decision of generation asset allocation and the relationship between futures contract price and spot price are tested and analyzed.

OPTIMAL PORTFOLIO CONSTRUCTION UNDER PARTIAL INFORMATION FOR A BALANCED FUND

The model parameters in optimal asset allocation problems are often assumed to be deterministic. This is not a realistic assumption since most parameters are not known exactly and therefore have to be estimated. We consider investment opportunities which are modeled as local geometric Brownian motions whose drift terms may be stochastic and not necessarily measurable. The drift terms of the risky assets are assumed to be affine functions of some arbitrary factors. These factors themselves may be stochastic processes. They are modeled to have a mean-reverting behavior. We consider two types of factors, namely observable and unobservable ones. The closed-form solution of the general problem is derived. The investor is assumed to have either constant relative risk aversion (CRRA) or constant absolute risk aversion (CARA). The optimal asset allocation under partial information is derived by transforming the problem into a full-information problem, where the solution is well known. The analytical result is empirically tested in a real-world application. In our case, we consider the optimal management of a balanced fund mandate. The unobservable risk factors are estimated with a Kalman filter. We compare the results of the partial-information strategy with the corresponding full-information strategy. We find that using a partial-information approach yields much better results in terms of Sharpe ratios than the full-information approach.

Incorporating Foreign Equities in the Optimal Asset Allocation of an Insurer with the Consideration for Background Risks: Models and Numerical Illustrations

We analyzes the optimal asset allocation problem for life insurers that are required to cope with significant background risks originating from life insurance businesses among a set of stochastic investment opportunities including foreign equities. The insurer is assumed to maximize the expected discounted utility of its surplus over a time horizon, and the optimalization problem is formulated in a stochastic control framework. Our derivations show that the optimal portfolio can be characterized by three components: a risk-minimizing component, a risk aversion index coupled with the portfolio’s performance index, and the component reflecting the diffusions of state variables. Since the explicit solutions cannot be derived due to the complexity of the model, we employ Markov chain approximation methods to obtain the optimal control solutions numerically. The model and numerical methods are then applied to a hypothetical insurer in a simplified setting as an illustrative example.