scholarly journals PORTFOLIO OPTIMIZATION IN A DEFAULT MODEL UNDER FULL/PARTIAL INFORMATION

2015 ◽  
Vol 29 (4) ◽  
pp. 565-587 ◽  
Author(s):  
Thomas Lim ◽  
Marie-Claire Quenez
Keyword(s):  
Utility Function ◽  
Partial Information ◽  
Backward Stochastic Differential Equation ◽  
Asset Price ◽  
Incomplete Market ◽  
Exponential Utility ◽  
Indifference Pricing ◽  
Insider Information ◽  
Default Time ◽  
Default Intensity

In this paper, we consider a financial market with an asset exposed to a risk inducing a jump in the asset price, and which can still be traded after the default time. We use a default-intensity modeling approach, and address in this incomplete market context the problem of maximization of expected utility from terminal wealth for logarithmic, power and exponential utility functions. We study this problem as a stochastic control problem both under full and partial information. Our contribution consists of showing that the optimal strategy can be obtained by a direct approach for the logarithmic utility function, and the value function for the power (resp. exponential) utility function can be determined as the minimal (resp. maximal) solution of a backward stochastic differential equation. For the partial information case, we show how the problem can be divided into two problems: a filtering problem and an optimization problem. We also study the indifference pricing approach to evaluate the price of a contingent claim in an incomplete market and the information price for an agent with insider information.

scholarly journals DEFAULTABLE CLAIMS IN SWITCHING MODELS WITH PARTIAL INFORMATION

2019 ◽  
Vol 22 (04) ◽  
pp. 1950006 ◽  
Author(s):  
PAVEL V. GAPEEV ◽  
MONIQUE JEANBLANC
Keyword(s):  
Drift Rate ◽  
Risk Model ◽  
Partial Information ◽  
Default Time ◽  
Default Intensity ◽  
Switching Models ◽  
Time Changes ◽  
The Times ◽  
Credit Risk Model ◽  
Default Intensity Process

We study a credit risk model for a financial market in which the local drift rate of the logarithm of the intensity of the default time changes at the times at which certain unobservable external events occur. The risk-neutral dynamics of the default intensity are described by a generalized geometric Brownian motion and the changes of the local drift rate arrive at independent exponential times. We obtain closed form expressions for the rational values of defaultable European-style contingent claims through the filtering estimates of the occurrence of switching times given the filtration generated by the default intensity process.

Information in Fleeting Opportunities

2013 ◽  
pp. 110-153
Author(s):  
Ibrahim Almojel ◽  
Jim Matheson ◽  
Pelin Canbolat
Keyword(s):  
Utility Function ◽  
Decision Maker ◽  
Optimal Policy ◽  
Value Of Information ◽  
Risk Preference ◽  
Dynamic Program ◽  
Exponential Utility ◽  
Venture Capitalists ◽  
Exponential Utility Function ◽  
Over Time

This paper focuses on the study of information in fleeting opportunities. An application example is the evaluation of business proposals by venture capitalists. The authors formulate the generic problem as a dynamic program where the decision maker can either accept a given deal directly, reject it directly, or seek further information on its potential and then decide whether to accept it or not. Results show well behaved characteristics of the optimal policy, deal flow value, and the value of information over time and capacity. It is presumed that the risk preference of the decision maker follows a linear or an exponential utility function. This approach is illustrated through several examples.

scholarly journals Explicit Pricing Formulas for European Option with Asset Exposed to Double Defaults Risk

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Taoshun He
Keyword(s):  
Default Risk ◽  
Asset Price ◽  
European Option ◽  
Put Options ◽  
Default Time ◽  
Novel Technique ◽  
Endogenous Default ◽  
Option Model ◽  
Analytical Formulas

We derive analytical formulas for European call and put options on underlying assets that are exposed to double defaults risks which include exogenous counterparty default risk and endogenous default risk. The endogenous default risk leads the asset price to drop to zero and the exogenous counterparty default risk induces a drop in the asset price, but the asset can still be traded after this default time. A novel technique is developed to evaluate the European call and put options by first conditioning on the predefault and the postdefault time and then obtaining the unconditional analytic formulas for their price. We also compare the pricing results of our model with default-free option model and counterparty default risk option model.

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