A new Bismut-Elworthy-Li-formula for diffusions with singular coefficients driven by a pure jump Levy process and applications to life insurance

The main result of my mine in the master thesis is a new Bismut-Elworthy-Li-formula with respect to a pure jump Levy noise driven stochastic differential equation (SDE), with non-Lipschitz continuous coefficients. This thesis consists of 5 chapters, where chapter 1 is an introduction to what Greeks...

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description The main result of my mine in the master thesis is a new Bismut-Elworthy-Li-formula with respect to a pure jump Levy noise driven stochastic differential equation (SDE), with non-Lipschitz continuous coefficients. This thesis consists of 5 chapters, where chapter 1 is an introduction to what Greeks are and why they are interesting in finance. In chapter 2 there is an overview and discussion of basic methods for the calculation of Greeks in the literature. In chapter 3 there is an implementation of what we refer to as Zhang s formula, namely a Bismut-Elworthy-Li type formula. This is a derivative free type formula for SDEs driven by pure jump process, namely an α-stable process. In the first part of chapter 3 simulations are conducted confirming that Zhang formula in numerical implementations works, then there is presented an application of this formula to life insurance, where we also conduct simulations. Chapter 4 is the highlight of this thesis, where we derive a BismutElworthy-Li type formula for the Greek Delta. This derivative free representation is obtained by using methods in [17] and [8]. The formula can be regarded as an extension of Zhang s formula in case of the Greek Delta, in the sense that we deal with Holder coefficients and don t demand that the coefficients have continuous first order derivative. Chapter 5 suggests possible extensions to this thesis.
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This thesis consists of 5 chapters, where chapter 1 is an introduction to what Greeks are and why they are interesting in finance. In chapter 2 there is an overview and discussion of basic methods for the calculation of Greeks in the literature. In chapter 3 there is an implementation of what we refer to as Zhang s formula, namely a Bismut-Elworthy-Li type formula. This is a derivative free type formula for SDEs driven by pure jump process, namely an α-stable process. In the first part of chapter 3 simulations are conducted confirming that Zhang formula in numerical implementations works, then there is presented an application of this formula to life insurance, where we also conduct simulations. Chapter 4 is the highlight of this thesis, where we derive a BismutElworthy-Li type formula for the Greek Delta. This derivative free representation is obtained by using methods in [17] and [8]. 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Chapter 5 suggests possible extensions to this thesis.</description><subject>Bismut</subject><subject>coefficients</subject><subject>diffusion</subject><subject>Elworthy</subject><subject>formula</subject><subject>Greeks</subject><subject>insurance</subject><subject>jump</subject><subject>Levy</subject><subject>life</subject><subject>linked</subject><subject>policies</subject><subject>pure</subject><subject>SDE</subject><subject>singular</subject><subject>unit</subject><fulltext>true</fulltext><rsrctype>dissertation</rsrctype><creationdate>2015</creationdate><recordtype>dissertation</recordtype><sourceid>3HK</sourceid><recordid>eNqFjDFOw0AQRd1QRIEz5F_AEgSikDKgIIqU9NayHpOJ1rOrmd1Y7iLlBNwjd8sViBA91Sve05tU32sIDXhh60uuN2GImndjveW6i9qX4HAlWr6cj8U4imHgvIOxfF2lwke6nE-eSbKhVT6Q4HOEQypK2Jc-YUuHEUmjJzM4aeFSCuxd_t3liMAdgcWKOvF0W910Lhjd_XFazd42H6_vtVe2zNJIVNc83D8v5s3TYr5cPf5f_ADeNFB_</recordid><startdate>2015</startdate><enddate>2015</enddate><creator>Christensen, Tor Martin</creator><scope>3HK</scope></search><sort><creationdate>2015</creationdate><title>A new Bismut-Elworthy-Li-formula for diffusions with singular coefficients driven by a pure jump Levy process and applications to life insurance</title><author>Christensen, Tor Martin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-cristin_nora_10852_452793</frbrgroupid><rsrctype>dissertations</rsrctype><prefilter>dissertations</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Bismut</topic><topic>coefficients</topic><topic>diffusion</topic><topic>Elworthy</topic><topic>formula</topic><topic>Greeks</topic><topic>insurance</topic><topic>jump</topic><topic>Levy</topic><topic>life</topic><topic>linked</topic><topic>policies</topic><topic>pure</topic><topic>SDE</topic><topic>singular</topic><topic>unit</topic><toplevel>online_resources</toplevel><creatorcontrib>Christensen, Tor Martin</creatorcontrib><collection>NORA - Norwegian Open Research Archives</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Christensen, Tor Martin</au><format>dissertation</format><genre>dissertation</genre><ristype>THES</ristype><btitle>A new Bismut-Elworthy-Li-formula for diffusions with singular coefficients driven by a pure jump Levy process and applications to life insurance</btitle><date>2015</date><risdate>2015</risdate><abstract>The main result of my mine in the master thesis is a new Bismut-Elworthy-Li-formula with respect to a pure jump Levy noise driven stochastic differential equation (SDE), with non-Lipschitz continuous coefficients. This thesis consists of 5 chapters, where chapter 1 is an introduction to what Greeks are and why they are interesting in finance. In chapter 2 there is an overview and discussion of basic methods for the calculation of Greeks in the literature. In chapter 3 there is an implementation of what we refer to as Zhang s formula, namely a Bismut-Elworthy-Li type formula. This is a derivative free type formula for SDEs driven by pure jump process, namely an α-stable process. In the first part of chapter 3 simulations are conducted confirming that Zhang formula in numerical implementations works, then there is presented an application of this formula to life insurance, where we also conduct simulations. Chapter 4 is the highlight of this thesis, where we derive a BismutElworthy-Li type formula for the Greek Delta. This derivative free representation is obtained by using methods in [17] and [8]. The formula can be regarded as an extension of Zhang s formula in case of the Greek Delta, in the sense that we deal with Holder coefficients and don t demand that the coefficients have continuous first order derivative. Chapter 5 suggests possible extensions to this thesis.</abstract><oa>free_for_read</oa></addata></record>
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source NORA - Norwegian Open Research Archives
subjects Bismut
coefficients
diffusion
Elworthy
formula
Greeks
insurance
jump
Levy
life
linked
policies
pure
SDE
singular
unit
title A new Bismut-Elworthy-Li-formula for diffusions with singular coefficients driven by a pure jump Levy process and applications to life insurance
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