Longevity-linked assets and pre-retirement consumption/portfolio decisions

We solve the consumption/investment problem of an agent facing a stochastic mortality intensity. The investment set includes a longevity-linked asset, as a derivative on the force of mortality. In a complete and frictionless market, we derive a closed form solution when the agent has Hyperbolic Absolute Risk Aversion preferences and a fixed financial horizon. Our calibrated numerical analysis on US data shows that individuals optimally invest a large fraction of their wealth in longevity-linked assets in the pre-retirement phase, because of their need to hedge against stochastic fluctuations in their remaining life-time at retirement.     

Improving the Graphical Lasso Estimation for the Precision Matrix Through Roots of the Sample Covariance Matrix

In this article, we focus on the estimation of a high-dimensional inverse covariance (i.e., precision) matrix. We propose a simple improvement of the graphical Lasso (glasso) framework that is able to attain better statistical performance without increasing significantly the computational cost. The proposed improvement is based on computing a root of the sample covariance matrix to reduce the spread of the associated eigenvalues. Through extensive numerical results, using both simulated and real datasets, we show that the proposed modification improves the glasso procedure. Our results reveal that the square-root improvement can be a reasonable choice in practice. Supplementary material for this article is available online.     

The optimal portfolio problem with coherent risk measure constraints

One of the basic problems of applied finance is the optimal selection of stocks, with the aim of maximizing future returns and constraining risks by an appropriate measure. Here, the problem is formulated by finding the portfolio that maximizes the expected return, with risks constrained by the worst conditional expectation. This model is a straightforward extension of the classic Markovitz mean–variance approach, where the original risk measure, variance, is replaced by the worst conditional expectation.The worst conditional expectation with a threshold α of a risk X, in brief WCE_α(X), is a function that belongs to the class of coherent risk measures. These are measures that satisfy a set of properties, such as subadditivity and monotonicity, that are introduced to prevent some of the drawbacks that affect some other common measures.This paper shows that the optimal portfolio selection problem can be formulated as a linear programming instance, but with an exponential number of constraints. It can be solved efficiently by an appropriate generation constraint subroutine, so that only a small number of inequalities are actually needed.This method is applied to the optimal selection of stocks in the Italian financial market and some computational results suggest that the optimal portfolios are better than the market index.     

An optimal portfolio model with stochastic volatility and stochastic interest rate

We consider a portfolio optimization problem under stochastic volatility as well as stochastic interest rate on an infinite time horizon. It is assumed that risky asset prices follow geometric Brownian motion and both volatility and interest rate vary according to ergodic Markov diffusion processes and are correlated with risky asset price. We use an asymptotic method to obtain an optimal consumption and investment policy and find some characteristics of the policy depending upon the correlation between the underlying risky asset price and the stochastic interest rate.     

VaR optimal portfolio with transaction costs

We consider the problem of portfolio optimization under VaR risk measure taking into account transaction costs. Fixed costs as well as impact costs as a nonlinear function of trading activity are incorporated in the optimal portfolio model. Thus the obtained model is a nonlinear optimization problem with nonsmooth objective function. The model is solved by an iterative method based on a smoothing VaR technique. We prove the convergence of the considered iterative procedure and demonstrate the nontrivial influence of transaction costs on the optimal portfolio weights.     

不确定条件下具有容差项的Markowitz证券组合投资模型的最优化解法

在分析证券市场中证券组合投资不确定性质的基础上,通过对Markowitz模型中证券期望收益与方差引入容差项来度量证券市场的不确定性,建立了不确定条件下具有容差项的Markowitz证券组合投资模型;分类讨论了容差的上界与下界所对应的两类有效组合前沿,得到了不确定条件下的证券组合投资模型的最优化解法及相关定理;最后给出了一个具体的数值实例．     

Investment models based on clustered scenario trees

Stochastic programming is widely applied in financial decision problems. In particular, when we need to carry out the actual calculations for portfolio selection problems, we have to assign a value for each expected return and the associated conditional probability in advance. These estimated random parameters often rely on a scenario tree representing the distribution of the underlying asset returns. One of the drawbacks is that the estimated parameters may be deviated from the actual ones. Therefore, robustness is considered so as to cope with the issue of parameter inaccuracy. In view of this, we propose a clustered scenario-tree approach, which accommodates the parameter inaccuracy problem in the context of a scenario tree.     

The role of index bonds in universal currency hedging

This study examines the demand for index bonds and their role in hedging risky asset returns against currency risks in a complete market where equity is not hedged against inflation risk. Avellaneda's uncertain volatility model with non-constant coefficients to describe equity price variation, forward price variation, index bond price variation and rate of inflation, together with Merton's intertemporal portfolio choice model, are utilized to enable an investor to choose an optimal portfolio consisting of equity, nominal bonds and index bonds when the rate of inflation is uncertain. A hedge ratio is universal if investors in different countries hedge against currency risk to the same extent. Three universal hedge ratios (UHRs) are defined with respect to the investor's total demand for index bonds, hedging risky asset returns (i.e. equity and nominal bonds) against currency risk, which are not held for hedging purposes. These UHRs are hedge positions in foreign index bond portfolios, stated as a fraction of the national market portfolio. At equilibrium all the three UHRs are comparable to Black's corrected equilibrium hedging ratio. The Cameron-Martin-Girsanov theorem is applied to show that the Radon-Nikodym derivative given under a P -martingale, the investor's exchange rate (product of the two currencies) is a martingale. Therefore the investors can agree on a common hedging strategy to trade exchange rate risk irrespective of investor nationality. This makes the choice of the measurement currency irrelevant and the hedge ratio universal without affecting their values.     

Risk‐based Decisions on the Asset Structure of a Bank under Partial Economic Information

We present a model of a bank's dynamic asset management problem in the case of partially observed future economic conditions and with regulatory requirements governing the level of risk taken. The result is an optimal control problem with a random terminal condition arising from the partial observation of a parameter of a maximized functional. The Stochastic Maximum Principle reduces the problem to finding a solution to a Forward Backward Stochastic Differential Equation (FBSDE). As optimization usually implies the dependence of the forward equation on solutions of the backward equation we allow the drift and diffusion of the forward part to be functions of the solution of the backward equation. The necessary conditions for the existence of solutions of FBSDE in such a form are derived. A numerical scheme is then implemented to solve a particular case.     

Building an Optimal Portfolio in Discrete Time in the Presence of Transaction Costs

Abstract

Portfolio theory covers different approaches to the construction of a portfolio offering maximum expected returns for a given level of risk tolerance where the goal is to find the optimal investment rule. Each investor has a certain utility for money which is reflected by the choice of a utility function. In this article, a risk averse power utility function is studied in discrete time for a large class of underlying probability distribution of the returns of the asset prices. Each investor chooses, at the beginning of an investment period, the feasible portfolio allocation which maximizes the expected value of the utility function for terminal wealth. Effects of both large and small proportional transaction costs on the choice of an optimal portfolio are taken into account. The transaction regions are approximated by using asymptotic methods when the proportional transaction costs are small and by using expansions about critical points for large transaction costs.