Related papers: Self-Financing Trading and the Ito-Doeblin Lemma
The paper tests the validity of the critique of the fiscal theory of the price level. A stochastic general equilibrium model with continuous time is constructed. An active fiscal policy and a passive monetary policy have been set. Monetary…
We present a financial market model, characterized by self-organized criticality, that is able to generate endogenously a realistic price dynamics and to reproduce well-known stylized facts. We consider a community of heterogeneous traders,…
Several versions of It\^{o}'s formula have been obtained in the context of the functional stochastic calculus. Here, we revisit this topic in two ways. First, by defining a notion of derivative along a functional, we extend the setting of…
It is well known that traded foreign exchange forwards and cross currency swaps (CCS) cannot be priced applying overnight cash and carry arguments as they imply absence of funding advantage of one currency to the other. This paper proposes…
The recent crash demonstrated (once again) that the description of the financial market by present financial mathematics cannot be considered as totally satisfactory. We remind that nowadays financial mathematics is heavily based on the use…
Trailing stop is a popular stop-loss trading strategy by which the investor will sell the asset once its price experiences a pre-specified percentage drawdown. In this paper, we study the problem of timing buy and then sell an asset subject…
This article studies convex duality in stochastic optimization over finite discrete-time. The first part of the paper gives general conditions that yield explicit expressions for the dual objective in many applications in operations…
We present an algorithm producing a dynamic non-self-financing hedging strategy in an incomplete market corresponding to investor-relevant risk criterion. The optimization is a two stage process that first determines admissible model…
The development of reinforced learning methods has extended application to many areas including algorithmic trading. In this paper trading on the stock exchange is interpreted into a game with a Markov property consisting of states,…
We present a non-probabilistic, pathwise approach to continuous-time finance based on causal functional calculus. We introduce a definition of self-financing, free from any integration concept and show that the value of a self-financing…
In academic literature portfolio risk management and hedging are often versed in the language of stochastic control and Hamilton--Jacobi--Bellman~(HJB) equations in continuous time. In practice the continuous-time framework of stochastic…
In this paper, making use of recent statistical physics techniques and models, we address the specific role of randomness in financial markets, both at the micro and the macro level. In particular, we review some recent results obtained…
Most of the existing literature on optimal trade execution in limit order book models assumes that resilience is positive. But negative resilience also has a natural interpretation, as it models self-exciting behaviour of the price impact,…
Fractional Brownian motion has become a standard tool to address long-range dependence in financial time series. However, a constant memory parameter is too restrictive to address different market conditions. Here we model the price…
Deep Learning is evolving fast and integrates into various domains. Finance is a challenging field for deep learning, especially in the case of interpretable artificial intelligence (AI). Although classical approaches perform very well with…
A classical inventory problem is studied from the perspective of embedded options, reducing inventory-management to the design of optimal contracts for forward delivery of stock (commodity). Financial option techniques \`{a} la…
We develop theory and applications of forward characteristic processes in discrete time following a seminal paper of Jan Kallsen and Paul Kr\"uhner. Particular emphasis is placed on the dynamics of volatility surfaces which can be easily…
We consider price competition among multiple sellers over a selling horizon of $T$ periods. In each period, sellers simultaneously offer their prices (which are made public) and subsequently observe their respective demand (not made…
We study, from the perspective of large financial markets, the asymptotic arbitrage opportunities in a sequence of binary markets approximating the fractional Black-Scholes model. This approximating sequence was introduced by Sottinen and…
This paper introduces a novel stochastic control framework to enhance the capabilities of automated investment managers, or robo-advisors, by accurately inferring clients' investment preferences from past activities. Our approach leverages…