Related papers: Valuations and dynamic convex risk measures
We consider the portfolio optimization with risk measured by conditional value-at-risk, based on the stress event of chosen asset being equal to the opposite of its value-at-risk level, under the normality assumption. Solvability conditions…
In this paper we analyze a dynamic recursive extension of the (static) notion of a deviation measure and its properties. We study distribution invariant deviation measures and show that the only dynamic deviation measure which is law…
We consider a trader who wants to direct his portfolio towards a set of acceptable wealths given by a convex risk measure. We propose a black-box algorithm, whose inputs are the joint law of stock prices and the convex risk measure, and…
Worst-case risk measures refer to the calculation of the largest value for risk measures when only partial information of the underlying distribution is available. For the popular risk measures such as Value-at-Risk (VaR) and Conditional…
Convexity, though extremely important in mathematical programming, has not drawn enough attention in the field of dynamic programming. This paper gives conditions for verifying convexity of the cost-to-go functions, and introduces an…
We consider the optimization of active extension portfolios. For this purpose, the optimization problem is rewritten as a stochastic programming model and solved using a clever multi-start local search heuristic, which turns out to provide…
We develop a method for computing policies in Markov decision processes with risk-sensitive measures subject to temporal logic constraints. Specifically, we use a particular risk-sensitive measure from cumulative prospect theory, which has…
We develop an averaging approach to robust risk measurement under payoff uncertainty. Instead of taking a worst-case value over an uncertainty neighborhood, we weight nearby payoffs more heavily under a chosen metric and average the…
We consider a collection of derivatives that depend on the price of an underlying asset at expiration or maturity. The absence of arbitrage is equivalent to the existence of a risk-neutral probability distribution on the price; in…
We propose a definition of diversification as a binary relationship between financial portfolios. According to it, a convex linear combination of several risk positions with some weights is considered to be less risky than the probabilistic…
We consider the convex set of positive operator valued measures (POVM) which are covariant under a finite dimensional unitary projective representation of a group. We derive a general characterization for the extremal points, and provide…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
The valuation of over-the-counter derivatives is subject to a series of valuation adjustments known as xVA, which pose additional risks for financial institutions. Associated risk measures, such as the value-at-risk of an underlying…
Multi-period measures of risk account for the path that the value of an investment portfolio takes. In the context of probabilistic risk measures, the focus has traditionally been on the magnitude of investment loss and not on the dimension…
We study the problem of portfolio insurance from the point of view of a fund manager, who guarantees to the investor that the portfolio value at maturity will be above a fixed threshold. If, at maturity, the portfolio value is below the…
We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their…
A generalization of expectiles for d-dimensional multivariate distribution functions is introduced. The resulting geometric expectiles are unique solutions to a convex risk minimization problem and are given by d-dimensional vectors. They…
In this paper, we endow the space of continuous translation invariant valuation on convex sets generated by mixed volumes coupled with a suitable Radon measure on tuples of convex bodies with two appropriate norms. This enables us to…
We propose a method to assess the intrinsic risk carried by a financial position $X$ when the agent faces uncertainty about the pricing rule assigning its present value. Our approach is inspired by a new interpretation of the quasiconvex…
A method for calculating multi-portfolio time consistent multivariate risk measures in discrete time is presented. Market models for $d$ assets with transaction costs or illiquidity and possible trading constraints are considered on a…