2022/02/06 by Mohammed Louriki, Louriki, Mohammed
Business, Management and Accounting · Decision Sciences · Economics, Econometrics and Finance · #Advanced Queuing Theory Analysis #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2202.02708
openalex publication_date 2022/02/06 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
We extend the information-based asset-pricing framework by Brody, Hughston & Macrina to incorporate a stochastic bankruptcy time for the writer of the asset. Our model introduces a non-defaultable cash flow ZT to be made at time T, alongside the time τ of a possible bankruptcy of the writer of the asset are in line with the filtration generated by a Brownian random bridge with length ν=τ\wedge T and pinning point σZT, where σ is a constant. Quantities ZT and τ are not necessarily independent. The model does not depend crucially on the interpretation of τ as a bankruptcy time. We derived the price process of the asset and compute the prices of associated options. The dynamics of the price process satisfy a diffusion equation. Employing the approach of P.-A.~ Meyer, we provide the explicit computation of the compensator of ν. Leveraging special properties of the bridge process, we also provide the explicit expression of the compensator of ZT \mathbbI[ν,+∞). The resulting conclusion highlights the totally inaccessible property of the stopping time ν. This characteristic is particularly suitable for financial markets where the time of default of a writer cannot be predictable from any other signal in the system until default happens.