Download Contract Theory in Continuous-Time Models by Jakša Cvitanic, Jianfeng Zhang PDF

By Jakša Cvitanic, Jianfeng Zhang

In fresh years there was an important raise of curiosity in continuous-time Principal-Agent types, or agreement conception, and their purposes. Continuous-time types supply a strong and chic framework for fixing stochastic optimization difficulties of discovering the optimum contracts among events, lower than quite a few assumptions at the details they've got entry to, and the influence they've got at the underlying "profit/loss" values. This monograph surveys contemporary result of the idea in a scientific method, utilizing the procedure of the so-called Stochastic greatest precept, in types pushed via Brownian Motion.

Optimal contracts are characterised through a method of Forward-Backward Stochastic Differential Equations. In a couple of attention-grabbing designated circumstances those could be solved explicitly, allowing derivation of many qualitative monetary conclusions.

Show description

Read or Download Contract Theory in Continuous-Time Models PDF

Similar game theory books

Differential Information Economies

One of many major difficulties in present monetary thought is to jot down contracts that are Pareto optimum, incentive suitable, and likewise implementable as an ideal Bayesian equilibrium of a dynamic, noncooperative online game. The query arises if it is attainable to supply Walrasian variety or cooperative equilibrium strategies that have those houses.

Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective

Rate of interest types: an enormous Dimensional Stochastic research viewpoint reviews the mathematical matters that come up in modeling the rate of interest time period constitution. those concerns are approached through casting the rate of interest types as stochastic evolution equations in endless dimensions. The publication is made from 3 components.

Strategy and Politics: An Introduction to Game Theory

Procedure and Politics: An creation to video game idea is designed to introduce scholars without history in formal idea to the appliance of online game concept to modeling political tactics. This obtainable textual content covers the basic features of online game conception whereas protecting the reader regularly involved with why political technology as a complete would get advantages from contemplating this system.

Extra resources for Contract Theory in Continuous-Time Models

Example text

1. This will be achieved if UP (XT − F (XT )) = zZ¯ T . 16) into account, we see that it is sufficient to have UP (x − F (x)) z = F (x). 17) Therefore, we get the following result. ; (iii) there exists a unique random variable XT = XT (y) that solves the first order condition; (iv) the constant y can be chosen so that the budget constraint E[Z¯ T XT ] = x is satisfied; (v) agent’s expected utility E[UA (F (XT ))] is the same as in the corresponding first best solution, that is, equal to E[UA (IA (zλ Z¯ T ))].

5) we obtain ∂X Uλ (X, G) = UP X − I (X, G) , ∂G Uλ (X, G) = λ∂G UA I (X, G), G . 4), we apply the method of the stochastic calculus of variations, which leads to the necessary conditions that go under the name the stochastic maximum principle, an analog to Pontryagin’s maximum principle in deterministic control. The method basically consists in finding the limits of finite differences of the processes involved, essentially differentiating the objective function, in order to get first order conditions for optimality.

5) we obtain ∂X Uλ (X, G) = UP X − I (X, G) , ∂G Uλ (X, G) = λ∂G UA I (X, G), G . 4), we apply the method of the stochastic calculus of variations, which leads to the necessary conditions that go under the name the stochastic maximum principle, an analog to Pontryagin’s maximum principle in deterministic control. The method basically consists in finding the limits of finite differences of the processes involved, essentially differentiating the objective function, in order to get first order conditions for optimality.

Download PDF sample

Rated 4.70 of 5 – based on 32 votes