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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…
We use generating functional analysis to study minority-game type market models with generalized strategy valuation updates that control the psychology of agents' actions. The agents' choice between trend following and contrarian trading,…
While investment funds publicly disclose their objectives in broad terms, their managers optimize for complex combinations of competing goals that go beyond simple risk-return trade-offs. Traditional approaches attempt to model this through…
The paper develops no arbitrage results for trajectory based models by imposing general constraints on the trading portfolios. The main condition imposed, in order to avoid arbitrage opportunities, is a local continuity requirement on the…
In order to simulate the complex phenomena manifested in stock markets, we introduce a continuous asynchronous model in which millions of individual traders interact through a central orders matching mechanism, just as it happens in real…
In this paper we propose a novel application of Gaussian processes (GPs) to financial asset allocation. Our approach is deeply rooted in Stochastic Portfolio Theory (SPT), a stochastic analysis framework introduced by Robert Fernholz that…
In the paper, the law of the iterated logarithm for additive functionals of Markov chains is obtained under some weak conditions, which are weaker than the conditions of invariance principle of additive functionals of Markov chains in M.…
The Mutual Fund Theorem (MFT) is considered in a general semimartingale financial market S with a finite time horizon T, where agents maximize expected utility of terminal wealth. It is established that: 1) Let N be the wealth process of…
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 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…
Generalized statistical arbitrage concepts are introduced corresponding to trading strategies which yield positive gains on average in a class of scenarios rather than almost surely. The relevant scenarios or market states are specified via…
We introduce predictable relative forward performance processes (PRFPP) as a new framework for studying portfolio management within a competitive and incomplete market environment. Each agent trades a distinct stock following a binomial…
This paper goes beyond the optimal trading Mean Field Game model introduced by Pierre Cardaliaguet and Charles-Albert Lehalle in [Cardaliaguet, P. and Lehalle, C.-A., Mean field game of controls and an application to trade crowding,…
We solve the problem of pricing and optimal exercise of American call-type options in markets which do not necessarily admit an equivalent local martingale measure. This resolves an open question proposed by Fernholz and Karatzas…
Whether you trade futures for yourself or a hedge fund, your strategy is counted. Long and short position limits make the number of unique strategies finite. Formulas of the numbers of strategies, transactions, do nothing actions are…
This study evaluates the practical usefulness of continuous-time arbitrage strategies designed to exploit serial correlation in fractional financial markets. Specifically, we revisit the strategies of Shiryaev (1998) and Salopek (1998) and…
We design a portfolio construction framework and implement an active investment strategy utilizing momentum and trend-following signals across multiple asset classes and asset class risk factors. We quantify the performance of this strategy…
The choice of admissible trading strategies in mathematical modelling of financial markets is a delicate issue, going back to Harrison and Kreps (1979). In the context of optimal portfolio selection with expected utility preferences this…
The solution existence of finite horizon optimal economic growth problems is studied by invoking Filippov's Existence Theorem for optimal control problems with state constraints of the Bolza type from the monograph of L. Cesari…
More than seventy years ago Harry Markowitz formulated portfolio construction as an optimization problem that trades off expected return and risk, defined as the standard deviation of the portfolio returns. Since then the method has been…