Mean-Variance portfolio optimization when each asset has individual uncertain exit-time

The standard Markowitz Mean-Variance optimization model is a single-period portfolio selection approach where the exit-time (or the time-horizon) is deterministic. ‎In this paper we study the Mean-Variance portfolio selection problem ‎with ‎uncertain ‎exit-time ‎when ‎each ‎has ‎individual uncertain ‎xit-time‎, ‎which generalizes the Markowitz's model‎. ‎‎‎‎‎‎We provide some conditions under which the optimal portfolio of the generalized problem is independent of the exit-times distributions. Also, ‎‎it is shown that under some general circumstances, the sets of optimal portfolios‎ ‎in the generalized model and the standard model are the same‎

Portfolio Strategy of Financial Market with Regime Switching Driven by Geometric Lévy Process

The problem of a portfolio strategy for financial market with regime switching driven by geometric Lévy process is investigated in this paper. The considered financial market includes one bond and multiple stocks which has few researches up to now. A new and general Black-Scholes (B-S) model is set up, in which the interest rate of the bond, the rate of return, and the volatility of the stocks vary as the market states switching and the stock prices are driven by geometric Lévy process. For the general B-S model of the financial market, a portfolio strategy which is determined by a partial differential equation (PDE) of parabolic type is given by using Itô formula. The PDE is an extension of existing result. The solvability of the PDE is researched by making use of variables transformation. An application of the solvability of the PDE on the European options with the final data is given finally

Tendencias y perspectivas de la ciencia financiera: Un artículo de revisión

Financial Science Trends and Perspectives: A Review Article Robert C. Merton's contributions are current. Regarding the design of retirement plans, in a framework of pension deficient systems, the investigations of Merton (1969) and (1971) on optimal consumption and portfolio rules during and after working life acquire contemporary validity. Likewise, Bodie and Merton (2002) propose the use of derivative products, at the international level, to diversify the risks of pension systems just at the moment when these systems of many underdeveloped and industrialized economies are on the verge of collapse; knowing that several of these systems only provide a meager proportion of the salary. Finally, Merton's theory of rational option pricing is retaken to create synthetic oil pipelines and power plants through the use of contingent claims. This paper aims to review the trends and perspectives in financial science and mathematical finance, within the framework of the pioneering contributions of Robert Cox Merton, highlighting priority areas that offer opportunities for research with social and global impacts.Las contribuciones de Robert C. Merton cobran vigencia actual. Con respecto del diseño de los planes para el retiro, en un marco de sistemas deficientes de pensiones, las investigaciones de Merton (1969) y (1971) sobre reglas óptimas de consumo y portafolio durante y después de la vida laboral cobran vigencia contemporánea. Asimismo, Bodie y Merton (2002) proponen el uso de productos derivados, en el ámbito internacional, para diversificar los riesgos de los sistemas de pensiones justo en el momento en que muchos de éstos, en economías subdesarrolladas e industrializadas, están en la antesala de colapso; además de que varios de estos sistemas sólo garantizan una proporción exigua del salario. Por último, la teoría racional de valuación de opciones de Merton (1973) se retoma para crear oleoductos y plantas generadoras de energía sintéticas  mediante el uso de contratos derivados. Este trabajo pretende realizar una revisión de las tendencias y perspectivas de la ciencia financiera y las finanzas matemáticas, en el marco de las contribuciones pioneras de Robert Cox Merton, resaltando áreas prioritarias que ofrecen oportunidades para realizar investigación con impactos social y global