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We investigate the use of Kelly's strategy in the construction of an optimal portfolio of assets. For lognormally distributed asset returns, we derive approximate analytical results for the optimal investment fractions in various settings.…
We consider the problem of governing systemic risk in a banking system model. The banking system model consists in an initial value problem for a system of stochastic differential equations whose dependent variables are the log-monetary…
We consider a stochastic game-theoretic model of an investment market in continuous time with short-lived assets and study strategies, called survival, which guarantee that the relative wealth of an investor who uses such a strategy remains…
Financial markets, with their vast range of different investment opportunities, can be seen as a system of many different simultaneous games with diverse and often unknown levels of risk and reward. We introduce generalizations to the…
We study the asymptotic behavior of the ratio of total return (or total profit) to total amount bet in a casino game. While the limit is well understood when the sequence of wagers is independent and identically distributed, here we…
This paper studies the dividend and capital injection problem under a diffusion risk model with general discount functions. A proportional cost is imposed when injecting capitals. For exponential discounting as time-consistent benchmark, we…
In this work, we consider rule-based investment strategies for managing a defined contribution saving scheme under the Dutch pension fund testing model. We found that dynamic rule-based investment can outperform traditional static…
Constrained Reinforcement Learning (CRL) is a subset of machine learning that introduces constraints into the traditional reinforcement learning (RL) framework. Unlike conventional RL which aims solely to maximize cumulative rewards, CRL…
By proving a local limit theorem for higher-order transitions, we determine the time required for necklace chains to be close to stationarity. Because necklace chains, built by arranging identical smaller chains around a directed cycle, are…
Revisiting the continuous-time Mean-Variance (MV) Portfolio Optimization problem, we model the market dynamics with a jump-diffusion process and apply Reinforcement Learning (RL) techniques to facilitate informed exploration within the…
Cryptocurrencies return cross-predictability and technological similarity yield information on risk propagation and market segmentation. To investigate these effects, we build a time-varying network for cryptocurrencies, based on the…
Cryptocurrencies return cross-predictability and technological similarity yield information on risk propagation and market segmentation. To investigate these effects, we build a time-varying network for cryptocurrencies, based on the…
Technical trading rules and linear regressive models are often used by practitioners to find trends in financial data. However, these models are unsuited to find non-linearly separable patterns. We propose a decision tree forecasting model…
This paper studies a two-person trading game in continuous time that generalizes Garivaltis (2018) to allow for stock prices that both jump and diffuse. Analogous to Bell and Cover (1988) in discrete time, the players start by choosing fair…
Risk and uncertainty will always be a matter of experience, luck, skills, and modelling. Leverage is another concept, which is critical for the investor decisions and results. Adaptive skills and quantitative probabilistic methods need to…
Ergodicity describes an equivalence between the expectation value and the time average of observables. Applied to human behaviour, ergodic theories of decision-making reveal how individuals should tolerate risk in different environments. To…
Interval bankruptcy problems arise in situations where an estate has to be liquidated among a fixed number of creditors and uncertainty about the amounts of the claims is modeled by intervals. We extend in the interval setting the classical…
We consider a robust consumption-investment problem under CRRA and CARA utilities. The time-varying confidence sets are specified by $\Theta$, a correspondence from $[0,T]$ to the space of L\'{e}vy triplets, and describe priori information…
The prospects of Kahneman and Tversky, Mega Million and Powerball lotteries, St. Petersburg paradox, premature profits and growing losses criticized by Livermore are reviewed under an angle of view comparing mathematical expectations with…
Earlier studies have shown that stock market distributions can be well described by distributions derived from Tsallis entropy, which is a generalization of Shannon entropy to non-extensive systems. In this paper, Tsallis relative entropy…