Optimal control of capital injections by reinsurance and investments [Elektronische Ressource] / vorgelegt von Julia Eisenberg

Optimal Control of Capital Injections byReinsurance and InvestmentsINAUGURAL-DISSERTATIONZURERLANGUNG DESDOKTORGRADES¨DERMATHEMATISCH-NATURWISSENSCHAFTLICHENFAKULTAT¨ ¨DERUNIVERSITAT ZUKOLNVORGELEGT VONJulia Eisenbergaus Asˇhabad1. Berichterstatter: Prof. Dr. Hanspeter Schmidli, Universit¨at zu K¨oln2. Berichterstatter: Prof. Dr. Josef G. Steinebach, Universit¨at zu K¨olnTag der mu¨ndlichen Pru¨fung: 04.02.2010AcknowledgementsIwouldliketoexpressmythankstomysupervisorProf. Dr. HanspeterSchmidli. Ihavegreatlyprofitedfromhishintsandsuggestionsgenerouslygivenduringourconversations.I am very grateful to Prof. Dr. Josef Steinebach who agreed to be coreferent.I would like to acknowledge Markus Schulz for his listening ear and Mrs Anderka forbelieving in me.In particular, I would like to thank my family who has supported me all the time andenabled a successful completion of this work.AbstractAn insurance company, having an initial capital x, cashes premiums continuously andpays claims of random sizes at random times. In addition to that, the company can buyreinsurance or/and invest money into a riskless or risky assets. The company holdersare confronted with the problem of taking decisions on a businesspolicy of the company.Thus, a measure for the risk connected with an insurance portfolio is sorely needed.The ruin probability, i.e.