Related papers: Analytic solution to variance optimization with no…
In this paper, we study two optimisation settings for an insurance company, under the constraint that the terminal surplus at a deterministic and finite time $T$ follows a normal distribution with a given mean and a given variance. In both…
We obtain distribution-free bounds for various fundamental quantities used in probability theory by solving optimization problems that search for extreme distributions among all distributions with the same mean and dispersion. These…
This article clarifies the relationship between pricing kernel monotonicity and the existence of opportunities for stochastic arbitrage in a complete and frictionless market of derivative securities written on a market portfolio. The…
This paper analyzes a problem of optimal static hedging using derivatives in incomplete markets. The investor is assumed to have a risk exposure to two underlying assets. The hedging instruments are vanilla options written on a single…
We study entropy-regularized mean-variance portfolio optimization under Bayesian drift uncertainty. Gaussian policies remain optimal under partial information, the value function is quadratic in wealth, and belief-dependent coefficients…
We study a family of optimal control problems in which one aims at minimizing a cost that mixes a quadratic control penalization and the variance of the system, both for finitely many agents and for the mean-field dynamics as their number…
We study a continuous-time portfolio optimization problem under an explicit constraint on the Deviation Conditional Value-at-Risk (DCVaR), defined as the difference between the CVaR and the expected terminal wealth. While the mean-CVaR…
It is well known that quantile regression model minimizes the portfolio extreme risk, whenever the attention is placed on the estimation of the response variable left quantiles. We show that, by considering the entire conditional…
The standard approach for constructing a Mean-Variance portfolio involves estimating parameters for the model using collected samples. However, since the distribution of future data may not resemble that of the training set, the…
The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce…
Classical mean-variance portfolio theory tells us how to construct a portfolio of assets which has the greatest expected return for a given level of return volatility. Utility theory then allows an investor to choose the point along this…
In this paper, we consider $n$ agents who invest in a general financial market that is free of arbitrage and complete. The aim of each investor is to maximize her expected utility while ensuring, with a specified probability, that her…
Many stochastic optimization algorithms work by estimating the gradient of the cost function on the fly by sampling datapoints uniformly at random from a training set. However, the estimator might have a large variance, which inadvertently…
We study a class of sampled stochastic optimization problems, where the underlying state process has diffusive dynamics of the mean-field type. We establish the existence of optimal relaxed controls when the sample set has finite size. The…
This paper investigates the robust optimal control of sampled-data stochastic systems with multiplicative noise and distributional ambiguity. We consider a class of discrete-time optimal control problems where the controller \emph{jointly}…
In this paper, we consider robust control using randomized algorithms. We extend the existing order statistics distribution theory to the general case in which the distribution of population is not assumed to be continuous and the order…
This study investigates a robust screening problem under distributional ambiguity, where a seller is uncertain about a buyer's true valuation distribution, knowing only that it lies near a reference distribution measured by the Wasserstein…
Chance constraints provide a principled framework to mitigate the risk of high-impact extreme events by modifying the controllable properties of a system. The low probability and rare occurrence of such events, however, impose severe…
A drawdown constraint forces the current wealth to remain above a given function of its maximum to date. We consider the portfolio optimisation problem of maximising the long-term growth rate of the expected utility of wealth subject to a…
The $\ell_0$-constrained mean-CVaR model poses a significant challenge due to its NP-hard nature, typically tackled through combinatorial methods characterized by high computational demands. From a markedly different perspective, we propose…