On investment and minimization of shortfall risk for a diffusion model with jumps and two interest rates via market completion

Kane, Selly; Melnikov, Alexander

doi:10.1090/s0094-9000-09-00763-7

Cited by 2 publications

(2 citation statements)

References 19 publications

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“…Proof. The proof follows a similar structure to the one presented by Kane and Melnikov [21] in the multi-dimensional case.…”

Section: The Shortfall Risk Minimization Problemmentioning

confidence: 69%

Pricing Contingent Claims in a Two-Interest-Rate Multi-Dimensional Jump-Diffusion Model via Market Completion

Melnikov,

Mohammadi Nejad

2024

AppliedMath

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This paper investigates a financial market where asset prices follow a multi-dimensional Brownian motion process and a multi-dimensional Poisson process characterized by diverse credit and deposit rates where the credit rate is higher than the deposit rate. The focus extends to evaluating European options by establishing upper and lower hedging prices through a transition to a suitable auxiliary market. Introducing a lemma elucidates the same solution to the pricing problem in both markets under specific conditions. Additionally, we address the minimization of shortfall risk and determine no-arbitrage price bounds within the framework of incomplete markets. This study provides a comprehensive understanding of the challenges posed by the multi-dimensional jump-diffusion model and varying interest rates in financial markets.

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“…Proof. The proof follows a similar structure to the one presented by Kane and Melnikov [21] in the multi-dimensional case.…”

Section: The Shortfall Risk Minimization Problemmentioning

confidence: 69%

Pricing Contingent Claims in a Two-Interest-Rate Multi-Dimensional Jump-Diffusion Model via Market Completion

Melnikov,

Mohammadi Nejad

2024

AppliedMath

Self Cite

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“…Proof. The proof follows a similar structure to the one presented by Kane and Melnikov [4] in the multi-dimensional case.…”

Section: The Shortfall Risk Minimization Problemmentioning

confidence: 69%

Pricing Contingent Claims in a Two-Interest Rate Multi-dimensional Jump-diffusion Model via Market Completion

Melnikov,

Mohammadi Nejad

2023

Preprint

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In this paper, we investigate a financial market in which asset prices evolve based on a multi-dimensional Brownian motion process and a multi-dimensional Poisson process with different credit and deposit rates We proceed to evaluate European options by establishing upper and lower hedging prices through a transition to a suitable auxiliary market. Additionally, we address the minimization of shortfall risk and no-arbitrage price bounds in incomplete markets within this framework.

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On investment and minimization of shortfall risk for a diffusion model with jumps and two interest rates via market completion

Abstract: Abstract. This paper deals with the problems of investment and shortfall risk minimization in the framework of a two-factor diffusion model with jumps and with different credit and deposit rates. The optimal strategies are derived by means of auxiliary completions of the initial market.

Cited by 2 publications

References 19 publications

Pricing Contingent Claims in a Two-Interest-Rate Multi-Dimensional Jump-Diffusion Model via Market Completion

Pricing Contingent Claims in a Two-Interest-Rate Multi-Dimensional Jump-Diffusion Model via Market Completion

Pricing Contingent Claims in a Two-Interest Rate Multi-dimensional Jump-diffusion Model via Market Completion

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