Super-hedging-pricing formulas and Immediate-Profit arbitrage for market models under random horizon
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arXiv
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| Format: | Preprint |
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2024
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| author | Choulli, Tahir Lepinette, Emmanuel |
| author_facet | Choulli, Tahir Lepinette, Emmanuel |
| contents | In this paper, we consider the discrete-time setting, and the market model described by (S,F,T)$. Herein F is the ``public" flow of information which is available to all agents overtime, S is the discounted price process of d-tradable assets, and T is an arbitrary random time whose occurrence might not be observable via F. Thus, we consider the larger flow G which incorporates F and makes T an observable random time. This framework covers the credit risk theory setting, the life insurance setting and the setting of employee stock option valuation. For the stopped model (S^T,G) and for various vulnerable claims, based on this model, we address the super-hedging pricing valuation problem and its intrinsic Immediate-Profit arbitrage (IP hereafter for short). Our first main contribution lies in singling out the impact of change of prior and/or information on conditional essential supremum, which is a vital tool in super-hedging pricing. The second main contribution consists of describing as explicit as possible how the set of super-hedging prices expands under the stochasticity of T and its risks, and we address the IP arbitrage for (S^T,G) as well. The third main contribution resides in elaborating as explicit as possible pricing formulas for vulnerable claims, and singling out the various informational risks in the prices' dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05713 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Super-hedging-pricing formulas and Immediate-Profit arbitrage for market models under random horizon Choulli, Tahir Lepinette, Emmanuel Mathematical Finance Optimization and Control Probability Pricing of Securities In this paper, we consider the discrete-time setting, and the market model described by (S,F,T)$. Herein 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 whose occurrence might not be observable via F. Thus, we consider the larger flow G which incorporates F and makes T an observable random time. This framework covers the credit risk theory setting, the life insurance setting and the setting of employee stock option valuation. For the stopped model (S^T,G) and for various vulnerable claims, based on this model, we address the super-hedging pricing valuation problem and its intrinsic Immediate-Profit arbitrage (IP hereafter for short). Our first main contribution lies in singling out the impact of change of prior and/or information on conditional essential supremum, which is a vital tool in super-hedging pricing. The second main contribution consists of describing as explicit as possible how the set of super-hedging prices expands under the stochasticity of T and its risks, and we address the IP arbitrage for (S^T,G) as well. The third main contribution resides in elaborating as explicit as possible pricing formulas for vulnerable claims, and singling out the various informational risks in the prices' dynamics. |
| title | Super-hedging-pricing formulas and Immediate-Profit arbitrage for market models under random horizon |
| topic | Mathematical Finance Optimization and Control Probability Pricing of Securities |
| url | https://arxiv.org/abs/2401.05713 |