Related papers: On the Black's equation for the risk tolerance fun…
Population risk is always of primary interest in machine learning; however, learning algorithms only have access to the empirical risk. Even for applications with nonconvex nonsmooth losses (such as modern deep networks), the population…
We study the sensitivity of the expected utility maximization problem in a continuous semi-martingale market with respect to small changes in the market price of risk. Assuming that the preferences of a rational economic agent are modeled…
We investigate optimal consumption and investment problems for a Black-Scholes market under uniform restrictions on Value-at-Risk and Expected Shortfall. We formulate various utility maximization problems, which can be solved explicitly. We…
We investigate a continuous-time investment-consumption problem with model uncertainty in a general diffusion-based market with random model coefficients. We assume that a power utility investor is ambiguity-averse, with the preference to…
This paper examines optimal risk sharing for empirically realistic risk attitudes, providing results on Pareto optimality, competitive equilibria, utility frontiers, and the first and second theorems of welfare. Contrary to common…
In this paper, we study the portfolio utility maximization in the case where the risky asset is driven by a Brownian motion and an independent homogeneous Poisson measure, with strategies that may include jump signals. This means that the…
This study investigates the influence of risk tolerance on the expected utility in the long run. We estimate the extent to which the expected utility of optimal portfolios is affected by small changes in the risk tolerance. For this…
We find the optimal indemnity to maximize the expected utility of terminal wealth of a buyer of insurance whose preferences are modeled by an exponential utility. The insurance premium is computed by a convex functional. We obtain a…
This paper addresses the log-optimal portfolio for a general semimartingale model. The most advanced literature on the topic elaborates existence and characterization of this portfolio under no-free-lunch-with-vanishing-risk assumption…
Paper is based on "The cost of illiquidity and its effects on hedging", L. C. G. Rogers and Surbjeet Singh, 2010. We generalize its thesis to constant elasticity model, which own previously used Black-Schoels model as a special case. The…
This paper studies the portfolio optimization problem when the investor's utility is general and the return and volatility of the risky asset are fast mean-reverting, which are important to capture the fast-time scale in the modeling of…
This work initiates research into the problem of determining an optimal investment strategy for investors with different attitudes towards the trade-offs of risk and profit. The probability distribution of the return values of the stocks…
We study a n-player and mean-field portfolio optimization problem under relative performance concerns with non-zero volatility, for wealth and consumption. The consistency assumption defining forward relative performance processes leads to…
Risk measures connect probability theory or statistics to optimization, particularly to convex optimization. They are nowadays standard in applications of finance and in insurance involving risk aversion. This paper investigates a wide…
In this paper, we study convex risk measures with weak optimal transport penalties. In a first step, we show that these risk measures allow for an explicit representation via a nonlinear transform of the loss function. In a second step, we…
Having a perfect model to compute the optimal policy is often infeasible in reinforcement learning. It is important in high-stakes domains to quantify and manage risk induced by model uncertainties. Entropic risk measure is an exponential…
Portfolio managers often evaluate performance relative to benchmark, usually taken to be the Standard & Poor 500 stock index fund. This relative portfolio wealth is defined as the absolute portfolio wealth divided by wealth from investing…
This paper considers consumption and portfolio optimization problems with recursive preferences in both infinite and finite time regions. Specially, the financial market consists of a risk-free asset and a risky asset that follows a general…
We study the optimal investment and proportional reinsurance problem of an insurance company, whose investment preferences are described via a forward dynamic utility of exponential type in a stochastic factor model allowing for a possible…
We study the sensitivity to estimation error of portfolios optimized under various risk measures, including variance, absolute deviation, expected shortfall and maximal loss. We introduce a measure of portfolio sensitivity and test the…