Search results for "Terminal value"
showing 6 items of 6 documents
A continuous time tug-of-war game for parabolic $p(x,t)$-Laplace type equations
2019
We formulate a stochastic differential game in continuous time that represents the unique viscosity solution to a terminal value problem for a parabolic partial differential equation involving the normalized $p(x,t)$-Laplace operator. Our game is formulated in a way that covers the full range $1<p(x,t)<\infty$. Furthermore, we prove the uniqueness of viscosity solutions to our equation in the whole space under suitable assumptions.
TUG-OF-WAR, MARKET MANIPULATION, AND OPTION PRICING
2014
We develop an option pricing model based on a tug-of-war game involving the the issuer and holder of the option. This two-player zero-sum stochastic differential game is formulated in a multi-dimensional financial market and the agents try, respectively, to manipulate/control the drift and the volatility of the asset processes in order to minimize and maximize the expected discounted pay-off defined at the terminal date $T$. We prove that the game has a value and that the value function is the unique viscosity solution to a terminal value problem for a partial differential equation involving the non-linear and completely degenerate parabolic infinity Laplace operator.
Stationary and Initial-Terminal Value Problem for Collective Decision Making via Mean-Field Games
2017
Given a large number of homogeneous players that are distributed across three possible states, we consider the problem in which these players have to control their transition rates, following some optimality criteria. The optimal transition rates are based on the players' knowledge of their current state and of the distribution of all the other players, thus introducing mean-field terms in the running and the terminal cost. The first contribution is a mean-field model that takes into account the macroscopic and the microscopic dynamics. The second contribution is the study of the mean-field equilibrium resulting from solving the initial-terminal value problem, involving the Kolmogorov equat…
Functional Data Analysis for Optimizing Strategies of Cash-Flow Management
2017
The cash management deals with problem of automating and managing cash-flow processes. Optimization of the management processes greatly reduces overall cash handling costs. The present analysis is an empirical study of cash flows, from and to bank branches, deriving an underlying theoretical framework, which can in a reasonable way be connected with the optimal strategy. Functional data analysis is considered an appropriate framework to analyze the dynamics of the time series behavior of cash flows: since the observations are not equally spaced in time and their number is different for each series, they are converted into a collection of random curves in a space spanned by finite dimensiona…
Local Expected Shortfall-Hedging
2001
This paper proposes a self-financing trading strategy that minimizes the expected shortfall locally when hedging a European contingent claim. A positive shortfall occurs if the hedger is not willing to follow a perfect hedging or a superhedging strategy. In contrast to the classical variance criterion, the expected shortfall criterion depends only on undesirable outcomes where the terminal value of the written option exceeds the terminal value of the hedge portfolio. Searching a strategy which minimizes the expected shortfall is equivalent to the iterative solution of linear programs whose number increases exponentially with respect to the number of trading dates. Therefore, we partition th…
The value relevance of earnings, operating cash flow and accruals: A study on UK data
2003
The purpose of the work reported in this paper is to establish the value relevance of earnings, operating cash flows and accruals for UK companies. Innovations in this paper are threefold: the use ...