A martingale concept for non-monotone information in a jump process framework

@article{Christiansen2018AMC,
  title={A martingale concept for non-monotone information in a jump process framework},
  author={Marcus C. Christiansen},
  journal={arXiv: Probability},
  year={2018}
}
The information dynamics in finance and insurance applications is usually modeled by a filtration. This paper looks at situations where information restrictions apply such that the information dynamics may become non-monotone. A fundamental tool for calculating and managing risks in finance and insurance are martingale representations. We present a general theory that extends classical martingale representations to non-monotone information generated by marked point processes. The central idea… 
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References

SHOWING 1-10 OF 37 REFERENCES
Comparisons for backward stochastic differential equations on Markov chains and related no-arbitrage conditions
Most previous contributions to BSDEs, and the related theories of nonlinear expectation and dynamic risk measures, have been in the framework of continuous time diffusions or jump diffusions. Using
Martingales on Jump Processes. I: Representation Results
The paper is a contribution to the theory of martingales of processes whose sample paths are piecewise constant and have finitely many discontinuities in a finite time interval. The assumption is
Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications: BSDEs with Jumps
Introduction.- Stochastic Calculus.- Backward Stochastic Differential Equations - the General Case.- Forward-Backward Stochastic Differential Equations.- Numerical Methods for FBSDEs.- Nonlinear
Optimal hedging of demographic risk in life insurance
A Markov chain model is taken to describe the development of a multi-state life insurance policy or portfolio in a stochastic economic–demographic environment. It is assumed that there exists an
The Markov Chain Market
We consider a financial market driven by a continuous time homogeneous Markov chain. Conditions for absence of arbitrage and for completeness are spelled out, non-arbitrage pricing of derivatives is
Anomalous PDEs in Markov chains: Domains of validity and numerical solutions
TLDR
This paper investigates the validity of these differential equations by locating the points of non-smoothness of the state-wise conditional expected values, and it presents a numerical method for computation of such expected values with a controlled global error.
A Markov Model for the Term Structure of Credit Risk Spreads
This paper provides a Markov model for the term structure of credit risk spreads. The model is based on Jarrow and Turnbull (1995) with the bankruptcy process following a discrete state space Markov
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