Related papers: Deterministic definition of the capital risk
Diffusion in a linear potential in the presence of position-dependent killing is used to mimic a default process. Different assumptions regarding transport coefficients, initial conditions, and elasticity of the killing measure lead to…
Taking the two-dimensional $\phi^4$ theory as an example, we numerically solve the deterministic equations of motion with random initial states. Short-time behavior of the solutions is systematically investigated. Assuming that the…
We consider an individual or household endowed with an initial capital and an income, modeled as a deterministic process with a continuous drift rate. At first, we model the discounting rate as the price of a zero-coupon bond at zero under…
Risk control has become one of the major concern of financial institutions. The need for adequate statistical tools to measure and anticipate the amplitude of the potential moves of financial markets is clearly expressed, in particular for…
We study an optimal investment/consumption problem in a model capturing market and credit risk dependencies. Stochastic factors drive both the default intensity and the volatility of the stocks in the portfolio. We use the martingale…
An asset pricing model using long-run capital share growth risk has recently been found to successfully explain U.S. stock returns. Our paper adopts a recursive preference utility framework to derive an heterogeneous asset pricing model…
We consider the problem of governing systemic risk in an assets-liabilities dynamical model of banking system. In the model considered each bank is represented by its assets and its liabilities.The capital reserves of a bank are the…
This paper presents a convenient framework for modeling default process and pricing derivative securities involving credit risk. The framework provides an integrated view of credit valuation adjustment by linking distance-to-default,…
This paper shows that with mechanistic primary budget rules and with some simple assumptions on interest rates the well-known debt dynamics equation transforms into the infamous logistic map. The logistic map has very peculiar and rich…
We investigate the dynamics of growth models in terms of dynamical system theory. We analyse some forms of knowledge and its influence on economic growth. We assume that the rate of change of knowledge depends on both the rate of change of…
In this paper we give definitions of matrix rates of return which do not depend on the choice of basis describing baskets. We give their economic interpretation. The matrix rate of return describes baskets of arbitrary type and extends…
In this paper, we deal with an axiomatic approach to default risk. We introduce the notion of a default risk measure, which generalizes the classical probability of default (PD), and allows to incorporate model risk in various forms. We…
We revisit two classical problems: the determination of the law of the underlying with respect to a risk-neutral measure on the basis of option prices, and the pricing of options with convex payoffs in terms of prices of call options with…
We show that classical particle mechanics (Hamiltonian and Lagrangian consistent with relativistic electromagnetism) can be derived from three fundamental assumptions: infinite reducibility, deterministic and reversible evolution, and…
We formulate a probabilistic Markov property in discrete time under a dynamic risk framework with minimal assumptions. This is useful for recursive solutions to risk-sensitive versions of dynamic optimisation problems such as optimal…
We introduce capital games, which generalize the definition of standard games to incorporate dynamics. In capital games, payoffs are in units of capital which are not assumed to be units of utility. The dynamics allow us to infer player…
We study optimal investment problem for a diffusion market consisting of a finite number of risky assets (for example, bonds, stocks and options). Risky assets evolution is described by Ito's equation, and the number of risky assets can be…
The aim of this paper is to introduce a new formalism for the deterministic analysis associated with backward stochastic differential equations driven by general c{\`a}dl{\`a}g martingales. When the martingale is a standard Brownian motion,…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
We study a stochastic recursive optimal control problem in which the cost functional is described by the solution of a backward stochastic differential equation driven by G-Brownian motion. Some of the economic and financial optimization…