Related papers: Risk-Constrained Kelly Gambling
More than seventy years ago Harry Markowitz formulated portfolio construction as an optimization problem that trades off expected return and risk, defined as the standard deviation of the portfolio returns. Since then the method has been…
Motivated by applications in clinical trials and finance, we study the problem of online convex optimization (with bandit feedback) where the decision maker is risk-averse. We provide two algorithms to solve this problem. The first one is a…
In this paper, both dynamic mean-variance portfolio selection problems and dynamic variance hedging problems are discussed under non-Markovian framework. Explicit closed-loop equilibrium strategies of these problems are respectively…
Multistage risk-averse optimal control problems with nested conditional risk mappings are gaining popularity in various application domains. Risk-averse formulations interpolate between the classical expectation-based stochastic and minimax…
We consider the problem of navigation with safety constraints. The safety constraints are probabilistic, where a given set is assigned a degree of safety, a number between zero and one, with zero being safe and one being unsafe. The…
This paper demonstrates a practical method for computing the solution of an expectation-constrained robust maximization problem with immediate applications to model-free no-arbitrage bounds and super-replication values for many financial…
We study the safe reinforcement learning problem with nonlinear function approximation, where policy optimization is formulated as a constrained optimization problem with both the objective and the constraint being nonconvex functions. For…
Chance constrained programming (CCP) refers to a type of optimization problem with uncertain constraints that are satisfied with at least a prescribed probability level. In this work, we study the sample average approximation (SAA) of…
Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…
Chance-constrained programs (CCP) represent a trade-off between conservatism and robustness in optimization. In many CCPs, one optimizes an objective under a probabilistic constraint continuously parameterized by a random vector $\xi$. In…
Chance constrained program where one seeks to minimize an objective over decisions which satisfy randomly disturbed constraints with a given probability is computationally intractable. This paper proposes an approximate approach to address…
A sequence of spin-1/2 particles polarised in one of two possible directions is presented to an experimenter, who can wager in a double-or-nothing game on the outcomes of measurements in freely chosen polarisation directions. Wealth is…
The takeoff point for this paper is the voluminous body of literature addressing recursive betting games with expected logarithmic growth of wealth being the performance criterion. Whereas almost all existing papers involve use of linear…
Mean-variance portfolio optimization problems often involve separable nonconvex terms, including penalties on capital gains, integer share constraints, and minimum position and trade sizes. We propose a heuristic algorithm for such problems…
Constrained Markov decision processes (CMDPs) are used as a decision-making framework to study the long-run performance of a stochastic system. It is well-known that a stationary optimal policy of a CMDP problem under discounted cost…
This paper considers risk-averse learning in convex games involving multiple agents that aim to minimize their individual risk of incurring significantly high costs. Specifically, the agents adopt the conditional value at risk (CVaR) as a…
In this paper, we consider the chance constrained based uncertain portfolio optimization problem in which the uncertain parameters are stochastic in nature. The primary goal of the work is to formulate the uncertain problem into a…
We consider a randomized algorithm for the unique games problem, using independent multinomial probabilities to assign labels to the vertices of a graph. The expected value of the solution obtained by the algorithm is expressed as a…
From the Hamilton-Jacobi-Bellman equation for the value function we derive a non-linear partial differential equation for the optimal portfolio strategy (the dynamic control). The equation is general in the sense that it does not depend on…
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…