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Multi-objective portfolio optimisation is a critical problem researched across various fields of study as it achieves the objective of maximising the expected return while minimising the risk of a given portfolio at the same time. However,…
We consider a dynamic portfolio optimization problem that incorporates predictable returns, instantaneous transaction costs, price impact, and stochastic volatility, extending the classical results of Garleanu and Pedersen (2013), which…
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…
Monotone mean-variance (MMV) utility is the minimal modification of the classical Markowitz utility that respects rational ordering of investment opportunities. This paper provides, for the first time, a complete characterization of optimal…
The aim of this paper is to study the optimal investment problem by using coherent acceptability indices (CAIs) as a tool to measure the portfolio performance. We call this problem the acceptability maximization. First, we study the…
The discrete-time mean-variance portfolio selection formulation, a representative of general dynamic mean-risk portfolio selection problems, does not satisfy time consistency in efficiency (TCIE) in general, i.e., a truncated pre-committed…
This paper develops a method to derive optimal portfolios and risk premia explicitly in a general diffusion model for an investor with power utility and a long horizon. The market has several risky assets and is potentially incomplete.…
In safety-critical decision-making, the environment may evolve over time, and the learner adjusts its risk level accordingly. This work investigates risk-averse online optimization in dynamic environments with varying risk levels, employing…
This paper solves a utility maximization problem under utility-based shortfall risk constraint, by proposing an approach using Lagrange multiplier and convex duality. Under mild conditions on the asymptotic elasticity of the utility…
We investigate the feasibility of integrating quantum algorithms as subroutines of simulation-based optimisation problems with relevance to and potential applications in mathematical finance. To this end, we conduct a thorough analysis of…
The Stochastic Shortest Path (SSP) problem models probabilistic sequential-decision problems where an agent must pursue a goal while minimizing a cost function. Because of the probabilistic dynamics, it is desired to have a cost function…
We introduce a new set of consistent measures of risks, in terms of the semi-invariants of pdf's, such that the centered moments and the cumulants of the portfolio distribution of returns that put more emphasis on the tail the…
We derive new results related to the portfolio choice problem for power and logarithmic utilities. Assuming that the portfolio returns follow an approximate log-normal distribution, the closed-form expressions of the optimal portfolio…
Motivated by the trade-off between exploitation and exploration in reinforcement learning, we study a continuous-time entropy-regularized mean variance portfolio selection problem in the presence of jumps. We propose an exploratory SDE for…
The geology of oil reservoirs is largely unknown. Consequently, the reservoir models used for production optimization are subject to significant uncertainty. To minimize the associated risk, the oil literature has mainly used ensemble-based…
We present a simulation-and-regression method for solving dynamic portfolio allocation problems in the presence of general transaction costs, liquidity costs and market impacts. This method extends the classical least squares Monte Carlo…
This paper is devoted to study the optimal portfolio problem. Harry Markowitz's Ph.D. thesis prepared the ground for the mathematical theory of finance. In modern portfolio theory, we typically find asset returns that are modeled by a…
In this work we present a model for the solution of the multi-period portfolio selection problem. The model is based on a time consistent dynamic risk measure. We apply l1-regularization to stabilize the solution process and to obtain…
We study a risk-constrained version of the stochastic shortest path (SSP) problem, where the risk measure considered is Conditional Value-at-Risk (CVaR). We propose two algorithms that obtain a locally risk-optimal policy by employing four…
Risk-sensitive control balances performance with resilience to unlikely events in uncertain systems. This paper introduces ergodic-risk criteria, which capture long-term cumulative risks through probabilistic limit theorems. By ensuring the…