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Designing an optimum portfolio for allocating suitable weights to its constituent assets so that the return and risk associated with the portfolio are optimized is a computationally hard problem. The seminal work of Markowitz that attempted…
Optimal portfolio selection problems are determined by the (unknown) parameters of the data generating process. If an investor wants to realise the position suggested by the optimal portfolios, he/she needs to estimate the unknown…
The purpose of this paper is to describe the numerical solution of the Hamilton-Jacobi-Bellman (HJB) for an optimal control problem for quantum spin systems. This HJB equation is a first order nonlinear partial differential equation defined…
This paper considers a utility maximization and optimal asset allocation problem in the presence of a stochastic endowment that cannot be fully hedged through trading in the financial market. After studying continuity properties of the…
We develop a non-parametric, semimartingale optimal transport, calibration methodology for local volatility models with stochastic interest rate. The method finds a fully calibrated model which is the closest, in a way that can be defined…
This paper examines a continuous time intertemporal consumption and portfolio choice problem with a stochastic differential utility preference of Epstein-Zin type for a robust investor, who worries about model misspecification and seeks…
We characterize the value of swing contracts in continuous time as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation with suitable boundary conditions. The case of contracts with penalties is straightforward, and in that…
We study the allocation of synthetic portfolios under hierarchical nested, one-factor, and diagonal structures of the population covariance matrix in a high-dimensional scenario. The noise reduction approaches for the sample realizations…
This study employs expected certainty equivalents to explore the reinsurance and investment issue pertaining to an insurer that aims to maximize the expected utility while being subject to random risk aversion. The insurer's surplus process…
Portfolio optimization has been an area that has attracted considerable attention from the financial research community. Designing a profitable portfolio is a challenging task involving precise forecasting of future stock returns and risks.…
We study optimal proportional reinsurance and investment strategies for an insurance company which experiences both ordinary and catastrophic claims and wishes to maximize the expected exponential utility of its terminal wealth. We propose…
This survey paper is focused on qualitative and numerical analyses of fully nonlinear partial differential equations of parabolic type arising in financial mathematics. The main purpose is to review various non-linear extensions of the…
Management of a portfolio that includes an illiquid asset is an important problem of modern mathematical finance. One of the ways to model illiquidity among others is to build an optimization problem and assume that one of the assets in a…
We study the problem of dynamically trading futures in a regime-switching market. Modeling the underlying asset price as a Markov-modulated diffusion process, we present a utility maximization approach to determine the optimal futures…
This paper studies an optimal dividend problem for a company that aims to maximize the mean-variance (MV) objective of the accumulated discounted dividend payments up to its ruin time. The MV objective involves an integral form over a…
Strategic asset allocation requires an investor to select stocks from a given basket of assets. The perspective of our investor is to maximize risk-adjusted alpha returns relative to a benchmark index. Historical returns are used to provide…
We study the design of portfolios under a minimum risk criterion. The performance of the optimized portfolio relies on the accuracy of the estimated covariance matrix of the portfolio asset returns. For large portfolios, the number of…
We present an accelerated algorithm for the solution of static Hamilton-Jacobi-Bellman equations related to optimal control problems. Our scheme is based on a classic policy iteration procedure, which is known to have superlinear…
The portfolio optimization problem in which the variances of the return rates of assets are not identical is analyzed in this paper using the methodology of statistical mechanical informatics, specifically, replica analysis. We define two…
It has been assumed that arbitrage profits are not possible in efficient markets, because future prices are not predictable. Here we show that predictability alone is not a sufficient measure of market efficiency. We instead propose to…