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Optimal investment, consumption and life insurance in a Lévy market
Dissertation (MSc)--University of Pretoria, 2016.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2015
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| _version_ | 1867613469166010368 |
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| access_status_str | Open Access |
| author2 | Kufakunesu, Rodwell |
| author_browse | Kufakunesu, Rodwell |
| author_facet | Kufakunesu, Rodwell |
| collection | Thesis |
| dc_rights_str_mv | © 2016 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Dissertation (MSc)--University of Pretoria, 2016. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/50312 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:36:38.421Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2015 |
| publishDateRange | 2015 |
| publishDateSort | 2015 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/50312 Optimal investment, consumption and life insurance in a Lévy market Kufakunesu, Rodwell Guambe, Calisto Mathematics of Finance UCTD Dissertation (MSc)--University of Pretoria, 2016. The purpose of this dissertation is to solve an optimal investment, consumption and life insurance problem described by jump-diffusion processes in two settings. First, we consider a problem with random parameters of a wage earner who wants to save to his beneficiary for his death. Using one risk-free asset and one risky asset price given by a geometric jump-diffusion process, we obtain the optimal strategy via the dynamic programming approach, combining the Hamilton-Jacobi-Bellman equation with a backward stochastic differential equation with jumps. Secondly, we discuss the optimal investment, consumption and life insurance problem with capital constraints. The problem consists of one risk-free asset and two risky asset prices defined in an independent Brownian motion and Poisson process. We derive the optimal strategy of the unconstrained problem via martingale approach, from which, the problem with capital constraint is solved applying the option based portfolio insurance method. Mathematics and Applied Mathematics MSc Unrestricted 2015-11-03T12:21:39Z 2015-11-03T12:21:39Z 2016-04 2016 Dissertation Guambe, C 2016, Optimal investment, consumption and life insurance in a Lévy market, MSc Dissertation, University of Pretoria, Pretoria, viewed yymmdd <http://hdl.handle.net/2263/50312> A2016 http://hdl.handle.net/2263/50312 en © 2016 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | Mathematics of Finance UCTD Optimal investment, consumption and life insurance in a Lévy market |
| title | Optimal investment, consumption and life insurance in a Lévy market |
| title_full | Optimal investment, consumption and life insurance in a Lévy market |
| title_fullStr | Optimal investment, consumption and life insurance in a Lévy market |
| title_full_unstemmed | Optimal investment, consumption and life insurance in a Lévy market |
| title_short | Optimal investment, consumption and life insurance in a Lévy market |
| title_sort | optimal investment consumption and life insurance in a levy market |
| topic | Mathematics of Finance UCTD |
| url | http://hdl.handle.net/2263/50312 |