2880. Super-hedging-pricing formulas for vulnerable claims or death derivatives in models with random horizon
Invited abstract in session WB-23: Optimization Models in Supply Chain and Financial Modeling, stream OR for Societal Development.
Wednesday, 10:30-12:00Room: Esther Simpson 3.01
Authors (first author is the speaker)
| 1. | Tahir Choulli
|
| Math and Stats Sciences, University of Alberta | |
| 2. | Emmanuel Lepinette
|
| CEREMADE, Dauphine University |
Abstract
We consider the market model described by the triplet (S, F,T). Here, F is the ``public" flow of information which is available to all agents overtime, S is the discounted price process of d-tradable assets, and T is an arbitrary random time which might not be observable via F. As random time can not be observed before it occurrence, the adequate larger flow G -that incorporates F and observes T when it occurs- is the progressive enlargement of F with T. This framework covers the credit risk setting where T represents the default time of a firm/client, the life insurance setting where T is the death time of an insured, and other areas of finance. We first address the existence of the super-hedging price as a price, which is intimately related to the absence of Immediate-Profit arbitrage (IP for short). Then we focus on elaborating explicit super-hedging formulas for various claims. Furthermore, we show how the super-hedging prices' set expands under the stochasticity of T. Finally, we quantify the impact of various risks induced by T on the super-hedging price of any vulnerable claim. This is achieved by decomposing its dynamics and singling out explicitly the various informational risks in the dynamics of the price process. This fact is vital when the insurance securitization process is adopted instead of the classical reinsurance process, towards amortizing the mortality and/or longevity risks . This talk is based on a joint work with Emmanuel Lepinette (Dauphine, France).
Keywords
- Stochastic Models
- Optimization in Financial Mathematics
- Risk Analysis and Management
Status: accepted
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