A stochastic portfolio optimization model with complete memory

In this article, we consider a portfolio optimization problem of the Merton’s type with complete memory over a finite time horizon. The problem is formulated as a stochastic control problem on a finite time horizon and the state evolves according to a process governed by a stochastic process with memory. The goal is to choose investment and consumption controls such that the total expected discounted utility is maximized. Under certain conditions, we derive the explicit solutions for the associated Hamilton–Jacobi–Bellman (HJB) equations in a finite-dimensional space for exponential, logarithmic, and power utility functions. For those utility functions, verification results are established to ensure that the solutions are equal to the value functions, and the optimal controls are also derived.     

Quadratic cone cutting surfaces for quadratic programs with on–off constraints

We study the convex hull of a set arising as a relaxation of difficult convex mixed integer quadratic programs (MIQP). We characterize the extreme points of the convex hull of the set and the extreme points of its continuous relaxation. We derive four quadratic cutting surfaces that improve the strength of the continuous relaxation. Each of the cutting surfaces is second-order-cone representable. Via a shooting experiment, we provide empirical evidence as to the importance of each inequality type in improving the relaxation. Computational results that employ the new cutting surfaces to strengthen the relaxation for MIQPs arising from portfolio optimization applications are promising.     

Some applications of L2-hedging with a non-negative wealth process

We consider the problem of L ²-hedging of contingent claims in diffusion type models for securities markets. In contrast to a recent paper of Schweizer (1994) we insist on a non-negative wealth process corresponding to the optimal hedge portfolio. For this reason the usual projection methods cannot be applied. We give some applications of L ²-hedging in this setting including hedging under constraints, a problem of approximating the wealth process of a richer investor and a mean-variance version of it.     

A machine learning efficient frontier

We propose a simple approach to bridge between portfolio theory and machine learning. The outcome is an out-of-sample machine learning efficient frontier based on two assets, high risk and low risk. By rotating between the two assets, we show that the proposed frontier dominates the mean–variance efficient frontier out-of-sample. Our results, therefore, shed important light on the appeal of machine learning into portfolio selection under estimation risk.     

Modeling partial Greeks of variable annuities with dependence

Dynamic hedging used to mitigate the financial risks associated with large portfolios of variable annuities requires calculating partial dollar deltas on major market indices. Metamodeling approaches have been proposed in the past few years to address the computational issues related to the calculation of partial dollar deltas. In this paper, we investigate whether the additional complication of modeling the dependence between the partial dollar deltas improves the accuracy of the metamodeling approaches. We use several copulas to model the dependence structures of the partial dollar deltas and conduct numerical experiments to compare different metamodels. Despite the evidence of strong dependence in the estimated models, our numerical results show that modeling the dependence structures in the metamodels does not improve the accuracy of the estimations at the portfolio level. This is because the dependence between the partial dollar deltas is well captured by the covariates used in the marginal models. This finding suggests that we should focus more on marginal models than specifying the dependence structure explicitly.     

Robust optimization and portfolio selection: The cost of robustness

Robust optimization is a tractable alternative to stochastic programming particularly suited for problems in which parameter values are unknown, variable and their distributions are uncertain. We evaluate the cost of robustness for the robust counterpart to the maximum return portfolio optimization problem. The uncertainty of asset returns is modelled by polyhedral uncertainty sets as opposed to the earlier proposed ellipsoidal sets. We derive the robust model from a min-regret perspective and examine the properties of robust models with respect to portfolio composition. We investigate the effect of different definitions of the bounds on the uncertainty sets and show that robust models yield well diversified portfolios, in terms of the number of assets and asset weights.     

Short sales in Log-robust portfolio management

This paper extends the Log-robust portfolio management approach to the case with short sales, i.e., the case where the manager can sell shares he does not yet own. We model the continuously compounded rates of return, which have been established in the literature as the true drivers of uncertainty, as uncertain parameters belonging to polyhedral uncertainty sets, and maximize the worst-case portfolio wealth over that set in a one-period setting. The degree of the manager’s aversion to ambiguity is incorporated through a single, intuitive parameter, which determines the size of the uncertainty set. The presence of short-selling requires the development of problem-specific techniques, because the optimization problem is not convex. In the case where assets are independent, we show that the robust optimization problem can be solved exactly as a series of linear programming problems; as a result, the approach remains tractable for large numbers of assets. We also provide insights into the structure of the optimal solution. In the case of correlated assets, we develop and test a heuristic where correlation is maintained only between assets invested in. In computational experiments, the proposed approach exhibits superior performance to that of the traditional robust approach.     

PORTFOLIO OPTIMIZATION TECHNIQUES FOR A MIXED‐GRAZING SCENARIO FOR AUSTRALIA'S RANGELANDS

Abstract Currently pastoralists in Australia view native mammal species as one of many variables that impact, usually negatively, on their productivity and therefore profitability. This does not necessarily have to be the case. The species with the largest impact, kangaroos, have a value that could be incorporated into their income stream as a method of both reducing risk and increasing biodiversity, and therefore increasing resilience. An investigation of the idea of optimally allocating stocking rates using techniques analogous to classical portfolio selection optimization is conducted. Using historical pricing data for beef, wool, and kangaroo meat, an efficient frontier is formed to analyze the best scenario dependent on an investors risk aversion. It is shown that there is a clear opportunity for pastoralists to benefit economically by the inclusion of kangaroos in a mixed‐grazing strategy for Australian rangelands.     

The credit risk+ model with general sector correlations

We consider an enhancement of the credit risk⁺ model to incorporate correlations between sectors. We model the sector default rates as linear combinations of a common set of independent variables that represent macro-economic variables or risk factors. We also derive the formula for exact VaR contributions at the obligor level.     

Formulation and computation of general financial equilibrium

In this paper a model of competitive financial equilibrium is introduced, which yields the optimal composition of assets and liabilities in each sector's portfolio, as well as the market clearing prices for each instrument. The variational inequality formulation of the equilibrium conditions is then utilized to establish existence and uniqueness properties of the solution pattern. Finally, an algorithm is proposed for the computation of the equilibrium pattern; the algorithm resolves the problem into simple network subproblems which can then be solved in closed form. The algorithm is then applied to an example.