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The theory of convex risk functions has now been well established as the basis for identifying the families of risk functions that should be used in risk averse optimization problems. Despite its theoretical appeal, the implementation of a…
Utility and risk are two often competing measurements on the investment success. We show that efficient trade-off between these two measurements for investment portfolios happens, in general, on a convex curve in the two dimensional space…
We derive new results related to the portfolio choice problem for power and logarithmic utilities. Assuming that the portfolio returns follow an approximate log-normal distribution, the closed-form expressions of the optimal portfolio…
We examine the problem of optimal portfolio allocation within the framework of utility theory. We apply exponential utility to derive the optimal diversification strategy and logarithmic utility to determine the optimal leverage. We enhance…
This paper studies an $\alpha$-robust utility maximization problem where an investor faces an intractable claim -- an exogenous contingent claim with known marginal distribution but unspecified dependence structure with financial market…
In this paper we develop a concrete and fully implementable approach to the optimization of functionally generated portfolios in stochastic portfolio theory. The main idea is to optimize over a family of rank-based portfolios parameterized…
We consider a discrete-time version of the popular optimal dividend pay-out problem in risk theory. The novel aspect of our approach is that we allow for a risk averse insurer, i.e., instead of maximising the expected discounted dividends…
We consider a single-period portfolio selection problem for an investor, maximizing the expected ratio of the portfolio utility and the utility of a best asset taken in hindsight. The decision rules are based on the history of stock returns…
We consider a utility-maximization problem in a general semimartingale financial model, subject to constraints on the number of shares held in each risky asset. These constraints are modeled by predictable convex-set-valued processes whose…
In this paper, we search for optimal portfolio strategies in the presence of various risk measure that are common in financial applications. Particularly, we deal with the static optimization problem with respect to Value at Risk, Expected…
This paper solves a utility maximization problem under utility-based shortfall risk constraint, by proposing an approach using Lagrange multiplier and convex duality. Under mild conditions on the asymptotic elasticity of the utility…
We consider the economic problem of optimal consumption and investment with power utility. We study the optimal strategy as the relative risk aversion tends to infinity or to one. The convergence of the optimal consumption is obtained for…
We consider the terminal wealth utility maximization problem from the point of view of a portfolio manager who is paid by an incentive scheme, which is given as a convex function $g$ of the terminal wealth. The manager's own utility…
We discuss a class of risk-sensitive portfolio optimization problems. We consider the portfolio optimization model investigated by Nagai in 2003. The model by its nature can include fixed income securities as well in the portfolio. Under…
Modern portfolio theory(MPT) addresses the problem of determining the optimum allocation of investment resources among a set of candidate assets. In the original mean-variance approach of Markowitz, volatility is taken as a proxy for risk,…
We revisit the problem of portfolio selection, where an investor maximizes utility subject to a risk constraint. Our framework is very general and accommodates a wide range of utility and risk functionals, including non-concave utilities…
In this paper, we consider a financial market with assets exposed to some risks inducing jumps in the asset prices, and which can still be traded after default times. We use a default-intensity modeling approach, and address in this…
We develop a general theory of risk measures that determines the optimal amount of capital to raise and invest in a portfolio of reference traded securities in order to meet a pre-specified regulatory requirement. The distinguishing feature…
We consider the problem of choosing a portfolio that maximizes the cumulative prospect theory (CPT) utility on an empirical distribution of asset returns. We show that while CPT utility is not a concave function of the portfolio weights, it…
The paper addresses the tolerance approach to the sensitivity analysis of optimal solutions to the nonlinear optimization problem of the form $$\mbox{$\bigoplus\limits_{y\in S}C(y)\to\min$\quad over\quad $S\in\mathcal{S}$,}$$ where…