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We review some fundamental concepts of investment from a mathematical perspective, concentrating specifically on fractional-Kelly portfolios, which allocate a fraction of wealth to a growth-optimal portfolio while the remainder collects (or…
Risk-only investment strategies have been growing in popularity as traditional in- vestment strategies have fallen short of return targets over the last decade. However, risk-based investors should be aware of four things. First,…
We attempt to mitigate the persistent tradeoff between risk and return in medium- to long-term portfolio management. This paper proposes a novel LLM-guided no-regret portfolio allocation framework that integrates online learning dynamics,…
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…
We discuss - in what is intended to be a pedagogical fashion - generalized "mean-to-risk" ratios for portfolio optimization. The Sharpe ratio is only one example of such generalized "mean-to-risk" ratios. Another example is what we term the…
Discrete time hedging in a complete diffusion market is considered. The hedge portfolio is rebalanced when the absolute difference between delta of the hedge portfolio and the derivative contract reaches a threshold level. The rate of…
We consider the classic Kelly gambling problem with general distribution of outcomes, and an additional risk constraint that limits the probability of a drawdown of wealth to a given undesirable level. We develop a bound on the drawdown…
We develop a new approach to solving classification problems, which is bases on the theory of coherent measures of risk and risk sharing ideas. The proposed approach aims at designing a risk-averse classifier. The new approach allows for…
Following several episodes of financial market turmoil in recent decades, changes in systemic risk have drawn growing attention. Therefore, we propose surveillance schemes for systemic risk, which allow to detect misspecified systemic risk…
Given two random realized returns on an investment, which is to be preferred? This is a fundamental problem in finance that has no definitive solution except in the case one investment always returns more than the other. In 1952 Markowitz…
This article investigates a regime-switching investment strategy aimed at mitigating downside risk by reducing market exposure during anticipated unfavorable market regimes. We highlight the statistical jump model (JM) for market regime…
A fractal approach to the long-short portfolio optimization is proposed. The algorithmic system based on the composition of market-neutral spreads into a single entity was considered. The core of the optimization scheme is a fractal walk…
This paper explores the applications of the 20/60/20 rule-a heuristic method that segments data into top-performing, average-performing, and underperforming groups-in mathematical finance. We review the statistical foundations of this rule…
In an incomplete market, including liquidly-traded European options in an investment portfolio could potentially improve the expected terminal utility for a risk-averse investor. However, unlike the Sharpe ratio, which provides a concise…
We characterize optimal monetary policy when policy endogenously moves risk premia through redistribution across agents who differ in their willingness to bear risk. The analytical core is Marginal Risk Capacity, the covariance of monetary…
In complete markets, there are risky assets and a riskless asset. It is assumed that the riskless asset and the risky asset are traded continuously in time and that the market is frictionless. In this paper, we propose a new method for…
Mid-cap companies, generally valued between \$2 billion and \$10 billion, provide investors with a well-rounded opportunity between the fluctuation of small-cap stocks and the stability of large-cap stocks. This research builds upon the…
There are various metrics for financial risk, such as value at risk (VaR), expected shortfall, expected/unexpected loss, etc. When estimating these metrics, it was very common to assume Gaussian distribution for the asset returns, which may…
A risk-neutral method is always used to price and hedge contingent claims in complete market, but another method based on utility maximization or risk minimization is wildly used in more general case. One can find all kinds of special risk…
It is widely known that the common risk-factors derived from PCA beyond the first eigenportfolio are generally difficult to interpret and thus to use in practical portfolio management. We explore a alternative approach (HPCA) which makes…