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Time-dynamic evaluations under non-monotone information generated by marked point processes

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  • Marcus C. Christiansen

    (Carl von Ossietzky Universität Oldenburg)

Abstract

The information dynamics in finance and insurance applications is usually modelled by a filtration. This paper looks at situations where information restrictions apply so 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 is to focus only on those properties that martingales and compensators show on infinitesimally short intervals. While classical martingale representations describe innovations only, our representations have an additional symmetric counterpart that quantifies the effect of information loss. We exemplify the results with examples from life insurance and credit risk.

Suggested Citation

  • Marcus C. Christiansen, 2021. "Time-dynamic evaluations under non-monotone information generated by marked point processes," Finance and Stochastics, Springer, vol. 25(3), pages 563-596, July.
    • Handle: RePEc:spr:finsto:v:25:y:2021:i:3:d:10.1007_s00780-021-00456-5
    DOI: 10.1007/s00780-021-00456-5
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    Cited by:

    1. Kristian Buchardt & Christian Furrer & Oliver Lunding Sandqvist, 2022. "Transaction time models in multi-state life insurance," Papers 2209.06902, arXiv.org, revised Feb 2023.

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    More about this item

    Keywords

    Credit risk modelling; Life insurance modelling; Information restrictions; Optional projections; Infinitesimal martingale representations;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G24 - Financial Economics - - Financial Institutions and Services - - - Investment Banking; Venture Capital; Brokerage

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