相关论文: The stochastic field of aggregate utilities and it…

In a stochastic volatility framework, we find a general pricing equation for the class of payoffs depending on the terminal value of a market asset and its final quadratic variation. This allows a pricing tool for European-style claims…

The paper generalizes the construction by stochastic flows of consistent utility processes introduced by M. Mrad and N. El Karoui in (2010). The utilities random fields are defined from a general class of processes denoted by $\GX$. Making…

We develop a single-period model for a large economic agent who trades with market makers at their utility indifference prices. A key role is played by a pair of conjugate saddle functions associated with the description of Pareto optimal…

This paper introduces stationary and multi-self-similar random fields which account for stochastic volatility and have type G marginal law. The stationary random fields are constructed using volatility modulated mixed moving average fields…

We propose functional approach to the stochastic inflationary universe dynamics. It is based on path integral representation of the solution to the differential equation for the scalar field probability distribution. In the saddle-point…

We derive a stochastic path integral representation of counting statistics in semi-classical systems. The formalism is introduced on the simple case of a single chaotic cavity with two quantum point contacts, and then further generalized to…

The integral with respect to a multidimensional stochastic measure, for which we assume only $\sigma$-additivity in probability, is studied. The continuity and differentiability of its realizations are established.

Studying sample path behaviour of stochastic fields/processes is a classical research topic in probability theory and related areas such as fractal geometry. To this end, many methods have been developed since a long time in Gaussian…

Motivated by the work of Musiela and Zariphopoulou \cite{zar-03}, we study the It\^o random fields which are utility functions $U(t,x)$ for any $(\omega,t)$. The main tool is the marginal utility $U_x(t,x)$ and its inverse expressed as the…

Existence of stochastic financial equilibria giving rise to semimartingale asset prices is established under a general class of assumptions. These equilibria are expressed in real terms and span complete markets or markets with withdrawal…

For $f,g:X\longrightarrow X$ continuous and commuting maps of a Hausdorff space, we investigate various conditions on $X$ and on the pair $(f,g)$ which provide existence of a coincidence value. We introduce generalized notions of the…

We use a path integral approach for solving the stochastic equations underlying the financial markets, and we show the equivalence between the path integral and the usual SDE and PDE methods. We analyze both the one-dimensional and the…

A deterministic system of coupled maps is proposed as a model for economic activity among interacting agents. The values of the maps represent the wealth of the agents. The dynamics of the system is controlled by two parameters. One…

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…

We present analytical investigations of a multiplicative stochastic process that models a simple investor dynamics in a random environment. The dynamics of the investor's budget, $x(t)$, depends on the stochasticity of the return on…

We investigate a classical lattice system with $N$ particles. The potential energy $V$ of the scalar displacements is chosen as a $\phi ^4$ on-site potential plus interactions. Its stationary points are solutions of a coupled set of…

Consider a discrete-time infinite horizon financial market model in which the logarithm of the stock price is a time discretization of a stochastic differential equation. Under conditions different from those given in a previous paper of…

This paper studies the problem of maximizing expected utility from terminal wealth in a semi-static market composed of derivative securities, which we assume can be traded only at time zero, and of stocks, which can be traded continuously…

This paper presents an identity between the multivariate and univariate saddlepoint approximations applied to sample path probabilities for a certain class of stochastic processes. This class, which we term the recursively compounded…

Stochastic volatility models describe asset prices $S_t$ as driven by an unobserved process capturing the random dynamics of volatility $\sigma_t$. Here, we quantify how much information about $\sigma_t$ can be inferred from asset prices…