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Stochastic optimal portfolios and life insurance problems in a Lévy market
Thesis (PhD)--University of Pretoria, 2018.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2018
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| _version_ | 1867613467009089536 |
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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 | © 2018 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 | Thesis (PhD)--University of Pretoria, 2018. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/65013 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:36:36.461Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2018 |
| publishDateRange | 2018 |
| publishDateSort | 2018 |
| 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:2263/65013 Stochastic optimal portfolios and life insurance problems in a Lévy market Kufakunesu, Rodwell calistoguambe@yahoo.com.br Guambe, Calisto UCTD Thesis (PhD)--University of Pretoria, 2018. This thesis solves various optimal investment, consumption and life insurance problems described by jump-diffusion processes. In the first part of the thesis, we solve an optimal investment, consumption, and life insurance problem when the investor is restricted to capital guarantee. We consider an incomplete market described by a jump-diffusion model with stochastic volatility. Using the martingale approach, we prove the existence of the optimal strategy and the optimal martingale measure and we obtain the explicit solutions for the power utility functions. Secondly, we prove the sufficient and necessary maximum principle for the similar problem proposed in the first part. Then we apply the results to solve an investment, consumption, and life insurance problem with stochastic volatility, that is, we consider a wage earner investing in one risk-free asset and one risky asset described by a jump-diffusion process and has to decide concerning consumption and life insurance purchase. We assume that the life insurance for the wage earner is bought from a market composed of M > 0 life insurance companies offering pairwise distinct life insurance contracts. The goal is to maximize the expected utilities derived from the consumption, the legacy in the case of a premature death and the investor's terminal wealth. The third part discusses an optimal investment, consumption and insurance problem of a wage earner under inflation. Assume a wage earner investing in a real money account and three asset prices, namely: a real zero coupon bond, the inflation-linked real money account and a risky share described by jump-diffusion processes. Using the theory of quadratic-exponential backward stochastic differential equation (BSDE) with jumps approach, we derive the optimal strategy for the two typical utilities (exponential and power) and the value function is characterized as a solution of BSDE with jumps. The explicit solutions for the optimal investment in both cases of exponential and power utility functions for a diffusion case are derived. Mathematics and Applied Mathematics PhD Unrestricted 2018-05-25T07:00:58Z 2018-05-25T07:00:58Z 2018-09 2018 Thesis Guambe, C 2018, Stochastic optimal portfolios and life insurance problems in a Lévy market, PhD Thesis, University of Pretoria, Pretoria, viewed yymmdd <http://hdl.handle.net/2263/65013> S2018 http://hdl.handle.net/2263/65013 en © 2018 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 | UCTD Stochastic optimal portfolios and life insurance problems in a Lévy market |
| title | Stochastic optimal portfolios and life insurance problems in a Lévy market |
| title_full | Stochastic optimal portfolios and life insurance problems in a Lévy market |
| title_fullStr | Stochastic optimal portfolios and life insurance problems in a Lévy market |
| title_full_unstemmed | Stochastic optimal portfolios and life insurance problems in a Lévy market |
| title_short | Stochastic optimal portfolios and life insurance problems in a Lévy market |
| title_sort | stochastic optimal portfolios and life insurance problems in a levy market |
| topic | UCTD |
| url | http://hdl.handle.net/2263/65013 |