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Solving large-scale robust portfolio optimization problems is challenging due to the high computational demands associated with an increasing number of assets, the amount of data considered, and market uncertainty. To address this issue, we…
In this paper, we consider the basic problem of portfolio construction in financial engineering, and analyze how market-based and analytical approaches can be combined to obtain efficient portfolios. As a first step in our analysis, we…
In the present paper, the primal-dual problem consisting of the investment risk minimization problem and the expected return maximization problem in the mean-variance model is discussed using replica analysis. As a natural extension of the…
We consider the problem of optimizing a portfolio of financial assets, where the number of assets can be much larger than the number of observations. The optimal portfolio weights require estimating the inverse covariance matrix of excess…
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…
In this paper, we study two classes of optimal reinsurance models from perspectives of both insurers and reinsurers by minimizing their convex combination where the risk is measured by a distortion risk measure and the premium is given by a…
We consider convex constrained optimization problems that also include a cardinality constraint. In general, optimization problems with cardinality constraints are difficult mathematical programs which are usually solved by global…
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…
A quadratic discrete time probabilistic model, for optimal portfolio selection in (re-)insurance is studied. For positive values of underwriting levels, the expected value of the accumulated result is optimized, under constraints on its…
Using a family of modified Weibull distributions, encompassing both sub-exponentials and super-exponentials, to parameterize the marginal distributions of asset returns and their natural multivariate generalizations, we give exact formulas…
The only input to attain the portfolio weights of global minimum variance portfolio (GMVP) is the covariance matrix of returns of assets being considered for investment. Since the population covariance matrix is not known, investors use…
This paper shows how to evolve numerically the maximum entropy probability distributions for a given set of constraints, which is a variational calculus problem. An evolutionary algorithm can obtain approximations to some well-known…
Graphical models are a powerful tool to estimate a high-dimensional inverse covariance (precision) matrix, which has been applied for a portfolio allocation problem. The assumption made by these models is a sparsity of the precision matrix.…
A discrete time probabilistic model, for optimal equity allocation and portfolio selection, is formulated so as to apply to (at least) reinsurance. In the context of a company with several portfolios (or subsidiaries), representing both…
This paper investigates a time-inconsistent portfolio selection problem in the incomplete mar ket model, integrating expected utility maximization with risk control. The objective functional balances the expected utility and variance on log…
We study optimal portfolio choice under Epstein-Zin recursive utility in the presence of general leverage constraints. We first establish that the optimal value function is the unique viscosity solution to the associated…
We study the problem of optimal portfolio selection under stochastic volatility within a continuous time reinforcement learning framework with portfolio constraints. Exploration is modeled through entropy-regularized relaxed controls, where…
We study an optimal consumption and investment problem in a possibly incomplete market with general, not necessarily convex, stochastic constraints. We give explicit solutions for investors with exponential, logarithmic and power utility.…
We introduce a solution scheme for portfolio optimization problems with cardinality constraints. Typical portfolio optimization problems are extensions of the classical Markowitz mean-variance portfolio optimization model. We solve such…
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…