The model considered here is essentially that formulated in the author's previous paper Conditions for Optimality in the Infinite-Horizon Portfolio-cum-Saving Problem with Semimartingale Investments, Stochastics and Stochastics Reports 29 (1990), 133-171. In this model, the vector process representing returns to investments is a general semimartingale. Processes defining portfolio plans are here required only to be predictable and non-negative. Existence of an optimal portfolio-cum-saving plan is proved under slight conditions of integrability imposed on the welfare functional; the proofs rely on properties of weak precompactness of portfolio and utility sequences in suitable L p spaces together with dominated and monotone convergence arguments. Conditions are also obtained for the uniqueness of the portfolio plan generating a given returns process (i.e. for the uniqueness of the integrands generating a given sum of semimartingale integrals) and for the uniqueness of an optimal plan; here use is made of random measures associated with the jumps of a semimartingale.
Financial Markets Group Discussion Papers DP 109