{"id":{"repo_id":"western-cape","oai_identifier":"oai:uwcscholar.uwc.ac.za:10566/22790"},"canonical_url":"https://search.dev.ndltd.org/etd/western-cape/oai:uwcscholar.uwc.ac.za:10566/22790","repository":{"repo_id":"western-cape","name":"University of the Western Cape","base_url":"https://uwcscholar.uwc.ac.za:8443/server/oai/request"},"display":{"title":"A mathematical model for managing equity-linked pensions","abstract":"Pension fund companies manage and invest large amounts of money on behalf of their members. In return for their contributions, members expect a benefit at termination of their contract. Due to the volatile nature of returns that pension funds attain, pension companies started attaching a minimum guaranteed amount to member’s benefits. In this mini-thesis we look at the pioneering work of Brennan and Schwartz [10] for pricing these minimum guarantees. The model they developed prices these minimum guarantees using option pricing theory. We also look at the model proposed by Deelstra et al. [13] which prices minimum guarantees in a stochastic financial setting. We conclude this mini-thesis with new contributions where we look at simple alternative ways of pricing minimum guarantees. We conclude this mini-thesis with an approach, related to the work of Brennan and Schwartz [10], whereby the member’s benefit is maximised for a given minimum guaranteed amount, which comprises of multi-period guarantees. We formulate a method to find the optimal stream of these multi-period guarantees.","abstract_html":"Pension fund companies manage and invest large amounts of money on behalf of their members. In return for their contributions, members expect a benefit at termination of their contract. Due to the volatile nature of returns that pension funds attain, pension companies started attaching a minimum guaranteed amount to member’s benefits. In this mini-thesis we look at the pioneering work of Brennan and Schwartz [10] for pricing these minimum guarantees. The model they developed prices these minimum guarantees using option pricing theory. We also look at the model proposed by Deelstra et al. [13] which prices minimum guarantees in a stochastic financial setting. We conclude this mini-thesis with new contributions where we look at simple alternative ways of pricing minimum guarantees. We conclude this mini-thesis with an approach, related to the work of Brennan and Schwartz [10], whereby the member’s benefit is maximised for a given minimum guaranteed amount, which comprises of multi-period guarantees. 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The model they developed prices these minimum guarantees using option pricing theory. We also look at the model proposed by Deelstra et al. [13] which prices minimum guarantees in a stochastic financial setting. We conclude this mini-thesis with new contributions where we look at simple alternative ways of pricing minimum guarantees. We conclude this mini-thesis with an approach, related to the work of Brennan and Schwartz [10], whereby the member’s benefit is maximised for a given minimum guaranteed amount, which comprises of multi-period guarantees. 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