Related papers: Portfolio Theory, Information Theory and Tsallis S…
This paper studies a continuous-time optimal portfolio selection problem in the complete market for a behavioral investor whose preference is of the prospect type with probability distortion. The investor concerns about the terminal…
We consider an investor faced with the utility maximization problem in which the risky asset price process has pure-jump dynamics affected by an unobservable continuous-time finite-state Markov chain, the intensity of which can also be…
We present a new framework for modeling the statistical behavior of both fully developed turbulence and short-term dynamics of financial markets based on the nonextensive thermostatistics proposed by Tsallis. We also show that intermittency…
The deviation of the efficient market hypothesis (EMH) for the practical economic system allows us gain the arbitrary or risk premium in finance markets. We propose the triplet $(R,H,\sigma)$ theory to give the local and global optimal…
Recent developments in deep learning techniques have motivated intensive research in machine learning-aided stock trading strategies. However, since the financial market has a highly non-stationary nature hindering the application of…
Cover's celebrated theorem states that the long run yield of a properly chosen "universal" portfolio is as good as the long run yield of the best retrospectively chosen constant rebalanced portfolio. The "universality" pertains to the fact…
We consider the problem of dynamic buying and selling of shares from a collection of $N$ stocks with random price fluctuations. To limit investment risk, we place an upper bound on the total number of shares kept at any time. Assuming that…
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…
We introduce a dynamic optimization framework to analyze optimal portfolio allocations within an information driven contagious distress model. The investor allocates his wealth across several stocks whose growth rates and distress…
We study the problem of optimal long term portfolio selection with a view to beat a benchmark. Two kinds of objectives are considered. One concerns the probability of outperforming the benchmark and seeks either to minimise the decay rate…
A competing market model with a polyvariant profit function that assumes "zeitnot" stock behavior of clients is formulated within the banking portfolio medium and then analyzed from the perspective of devising optimal strategies. An…
We study a mean-field version of rank-based models of equity markets such as the Atlas model introduced by Fernholz in the framework of Stochastic Portfolio Theory. We obtain an asymptotic description of the market when the number of…
In a reinforcement learning (RL) framework, we study the exploratory version of the continuous time expected utility (EU) maximization problem with a portfolio constraint that includes widely-used financial regulations such as short-selling…
This paper addresses the question of how to invest in a robust growth-optimal way in a market where the instantaneous expected return of the underlying process is unknown. The optimal investment strategy is identified using a generalized…
Portfolio optimization is a critical task in investment. Most existing portfolio optimization methods require information on the distribution of returns of the assets that make up the portfolio. However, such distribution information is…
The necessary information for specifying a complex system may not be completely accessible to us, i.e., to mathematical treatments. This is not to be confounded with the incompleteness of our knowledge about whatever systems or nature,…
In this work, we introduce Modern Portfolio Theory using basic concepts from linear algebra, differential calculus, statistics, and optimization. This theory allows us to measure the return and risk of an investment portfolio, serving as a…
Stochastic portfolio theory aims at finding relative arbitrages, i.e. trading strategies which outperform the market with probability one. Functionally generated portfolios, which are deterministic functions of the market weights, are an…
This paper investigates the optimal selection of portfolios for power utility maximizing investors in a financial market where stock returns depend on a hidden Gaussian mean reverting drift process. Information on the drift is obtained from…
Turnpike theorems state that if an investor's utility is asymptotically equivalent to a power utility, then the optimal investment strategy converges to the CRRA strategy as the investment horizon tends to infinity. This paper aims to…