Related papers: Risk-Constrained Kelly Gambling
We consider multi-agent decision making where each agent optimizes its convex cost function subject to individual and coupling constraints. The constraint sets are compact convex subsets of a Euclidean space. To learn Nash equilibria, we…
A continuous-time financial portfolio selection model with expected utility maximization typically boils down to solving a (static) convex stochastic optimization problem in terms of the terminal wealth, with a budget constraint. In…
In this work we consider optimal stopping problems with conditional convex risk measures called optimised certainty equivalents. Without assuming any kind of time-consistency for the underlying family of risk measures, we derive a novel…
The aim of this paper is to provide several examples of convex risk measures necessary for the application of the general framework for portfolio theory of Maier-Paape and Zhu, presented in Part I of this series (arXiv:1710.04579…
Betting markets are gaining in popularity. Mean beliefs generally differ from prices in prediction markets. Logarithmic utility is employed to study the risk and return adjustments to prices. Some consequences are described. A modified…
This article develops the theory of risk budgeting portfolios, when we would like to impose weight constraints. It appears that the mathematical problem is more complex than the traditional risk budgeting problem. The formulation of the…
We investigate the performance of the Kelly rule in a setting in which the dynamics of the return is represented by a time change process. We find that in this general semi-martingale setting the Kelly rule does not maximize the average…
We consider an investor who seeks to maximize her expected utility derived from her terminal wealth relative to the maximum performance achieved over a fixed time horizon, and under a portfolio drawdown constraint, in a market with local…
This paper develops a unified framework for zero-sum games in which both the pure strategies and the payoff matrices contain complex-valued entries. By leveraging a linear isomorphism between complex and real vector spaces, we extend key…
Optimization of conditional convex risk measure is a central theme in dynamic portfolio selection theory, which has not yet systematically studied in the previous literature perhaps since conditional convex risk measures are neither random…
We consider continuous-time mean-variance portfolio selection with bankruptcy prohibition under convex cone portfolio constraints. This is a long-standing and difficult problem not only because of its theoretical significance, but also for…
We consider a distributionally robust second-order stochastic dominance constrained optimization problem. We require the dominance constraints hold with respect to all probability distributions in a Wasserstein ball centered at the…
We define and develop an approach for risk budgeting allocation - a risk diversification portfolio strategy - where risk is measured using a dynamic time-consistent risk measure. For this, we introduce a notion of dynamic risk contributions…
Financial markets, with their vast range of different investment opportunities, can be seen as a system of many different simultaneous games with diverse and often unknown levels of risk and reward. We introduce generalizations to the…
In the online portfolio optimization framework, existing learning algorithms generate strategies that yield significantly poorer cumulative wealth compared to the best constant rebalancing portfolio in hindsight, despite being consistent in…
In this paper we present an evolutionary optimization approach to solve the risk parity portfolio selection problem. While there exist convex optimization approaches to solve this problem when long-only portfolios are considered, the…
In decision-making problems under uncertainty, probabilistic constraints are a valuable tool to express safety of decisions. They result from taking the probability measure of a given set of random inequalities depending on the decision…
The aims of this study are twofold. First, we consider an optimal risk allocation problem with non-convex preferences. By establishing an infimal representation for distortion risk measures, we give some necessary and sufficient conditions…
Many high dimensional sparse learning problems are formulated as nonconvex optimization. A popular approach to solve these nonconvex optimization problems is through convex relaxations such as linear and semidefinite programming. In this…
We develop the idea of using Monte Carlo sampling of random portfolios to solve portfolio investment problems. In this first paper we explore the need for more general optimization tools, and consider the means by which constrained random…