Related papers: Portfolio Optimization with Cumulative Prospect Th…
In this paper we consider a generalization of the Markowitz's Mean-Variance model under linear transaction costs and cardinality constraints. The cardinality constraints are used to limit the number of assets in the optimal portfolio. The…
Utility based methods provide a very general theoretically consistent approach to pricing and hedging of securities in incomplete financial markets. Solving problems in the utility based framework typically involves dynamic programming,…
The paper studies problem of continuous time optimal portfolio selection for a incom- plete market diffusion model. It is shown that, under some mild conditions, near optimal strategies for investors with different performance criteria can…
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…
Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave…
Financial portfolio optimization is a widely studied problem in mathematics, statistics, financial and computational literature. It adheres to determining an optimal combination of weights associated with financial assets held in a…
The fundamental principle in Modern Portfolio Theory (MPT) is based on the quantification of the portfolio's risk related to performance. Although MPT has made huge impacts on the investment world and prompted the success and prevalence of…
In spite of the growing consideration for optimal execution in the financial mathematics literature, numerical approximations of optimal trading curves are almost never discussed. In this article, we present a numerical method to…
A decision tree is commonly restricted to use a single hyperplane to split the covariate space at each of its internal nodes. It often requires a large number of nodes to achieve high accuracy, hurting its interpretability. In this paper,…
In this article, we study the generalized modern portfolio theory, with utility functions admitting higher-order cumulants. We establish that under certain genericity conditions, the utility function has a constant number of complex…
Many different approaches for solving Constraint Satisfaction Problems (CSPs) and related Constraint Optimization Problems (COPs) exist. However, there is no single solver (nor approach) that performs well on all classes of problems and…
This paper studies some unconventional utility maximization problems when the ratio type relative portfolio performance is periodically evaluated over an infinite horizon. Meanwhile, the agent is prohibited from short-selling stocks. Our…
We present a framework for modeling asset and portfolio dynamics, incorporating this information into portfolio optimization. For this framework, we introduce the Commonality Principle, providing a solution for the optimal selection of…
Approximations of functions with finite data often do not respect certain "structural" properties of the functions. For example, if a given function is non-negative, a polynomial approximation of the function is not necessarily also…
We examine the problem of optimal portfolio allocation within the framework of utility theory. We apply exponential utility to derive the optimal diversification strategy and logarithmic utility to determine the optimal leverage. We enhance…
We consider the problem of maximizing the asymptotic growth rate of an investor under drift uncertainty in the setting of stochastic portfolio theory (SPT). As in the work of Kardaras and Robertson we take as inputs (i) a Markovian…
We extend Relative Robust Portfolio Optimisation models to allow portfolios to optimise their distance to a set of benchmarks. Portfolio managers are also given the option of computing regret in a way which is more in line with market…
A novel optimisation framework through quadratic nonlinear projection is introduced for credit portfolio when the portfolio risk is measured by Conditional Value-at-Risk (CVaR). The whole optimisation procedure to search toward the optimal…
Portfolio managers often evaluate performance relative to benchmark, usually taken to be the Standard & Poor 500 stock index fund. This relative portfolio wealth is defined as the absolute portfolio wealth divided by wealth from investing…
Portfolio optimisation is essential in quantitative investing, but its implementation faces several practical difficulties. One particular challenge is converting optimal portfolio weights into real-life trades in the presence of realistic…