Real indeterminacy in incomplete financial market economies without aggregate risk

1991 ◽  
Vol 1 (3) ◽  
pp. 265-276 ◽  
Author(s):  
P. Siconolfi ◽  
A. Villanacci
Keyword(s):  
Financial Market ◽  
Market Economies ◽  
Aggregate Risk ◽  
Incomplete Financial Market ◽  
Real Indeterminacy

Backward Stochastic PDE and Imperfect Hedging

2003 ◽  
Vol 06 (07) ◽  
pp. 663-692 ◽  
Author(s):  
M. Mania ◽  
R. Tevzadze
Keyword(s):  
Financial Market ◽  
Asset Prices ◽  
Random Function ◽  
Value Function ◽  
Market Model ◽  
Stochastic Pde ◽  
Continuous Semimartingale ◽  
Incomplete Financial Market ◽  
Mean Variance ◽  
The Value Function

We consider a problem of minimization of a hedging error, measured by a positive convex random function, in an incomplete financial market model, where the dynamics of asset prices is given by an Rd-valued continuous semimartingale. Under some regularity assumptions we derive a backward stochastic PDE for the value function of the problem and show that the strategy is optimal if and only if the corresponding wealth process satisfies a certain forward-SDE. As an example the case of mean-variance hedging is considered.

RECURSIVE BACKWARD SCHEME FOR THE SOLUTION OF A BSDE WITH A NON LIPSCHITZ GENERATOR

2017 ◽  
Vol 31 (2) ◽  
pp. 207-225
Author(s):  
Paola Tardelli
Keyword(s):  
Unique Solution ◽  
Financial Market ◽  
Utility Maximization ◽  
Value Function ◽  
Jump Processes ◽  
Maximization Problem ◽  
Admissible Strategies ◽  
Incomplete Financial Market ◽  
Utility Maximization Problem ◽  
The Value Function

On an incomplete financial market, the stocks are modeled as pure jump processes subject to defaults. The exponential utility maximization problem is investigated characterizing the value function in term of Backward Stochastic Differential Equations (BSDEs), driven by pure jump processes. In general, in this setting, there is no unique solution. This is the reason why, the value function is proven to be the limit of a sequence of processes. Each of them is the solution of a Lipschitz BSDE and it corresponds to the value function associated with a subset of bounded admissible strategies. Given a representation of the jump processes driving the model, the aim of this note is to give a recursive backward scheme for the value function of the initial problem.

PARTIAL EQUILIBRIUM AND MARKET COMPLETION

2005 ◽  
Vol 08 (04) ◽  
pp. 483-508 ◽  
Author(s):  
YING HU ◽  
PETER IMKELLER ◽  
MATTHIAS MÜLLER
Keyword(s):  
Financial Market ◽  
Market Price ◽  
External Source ◽  
Partial Equilibrium ◽  
Individual Risk ◽  
Market Price Of Risk ◽  
Price Of Risk ◽  
Incomplete Financial Market ◽  
External Risk ◽  
The One

We consider financial markets with agents exposed to an external source of risk which cannot be hedged through investments on the capital market alone. The sources of risk we think of may be weather and climate. Therefore we face a typical example of an incomplete financial market. We design a model of a market on which the external risk becomes tradable. In a first step we complete the market by introducing an extra security which valuates the external risk through a process parameter describing its market price. If this parameter is fixed, risk has a price and every agent can maximize the expected exponential utility with individual risk aversion obtained from his risk exposure on the one hand and his investment into the financial market consisting of an exogenous set of stocks and the insurance asset on the other hand. In the second step, the market price of risk parameter has to be determined by a partial equilibrium condition which just expresses the fact that in equilibrium the market is cleared of the second security. This choice of market price of risk is performed in the framework of nonlinear backwards stochastic differential equations.

Sign in / Sign up

Export Citation Format

Share Document