Preservation of WSAI under default transforms and its application in allocating assets with dependent realizable returns

Financial instruments traded in the market are usually subject to mutually dependent default risks, and a default does not always make a zero return for the concerned risky asset. This paper revisits the portfolio selection problem with assets exposed to dependent default risks. To better model the default mechanism, we generalize the threshold default model and the independence default model due to Cheung and Yang (2004) by introducing a smaller nonzero realizable return for a default risky asset. By utilizing stochastic arrangement increasing techniques, we develop sufficient conditions to enable actuaries to order the amount allocated to each asset in the two generalized models. Also, some examples of dependence structures fulfilling the sufficient conditions are presented as illustrations.