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The purpose of this paper relies on the study of long term affine yield curves modeling. It is inspired by the Ramsey rule of the economic literature, that links discount rate and marginal utility of aggregate optimal consumption. For such a long maturity modelization, the possibility of adjusting preferences to new economic information is crucial, justifying the use of progressive utility. This paper studies, in a framework with affine factors, the yield curve given from the Ramsey rule. It first characterizes consistent progressive utility of investment and consumption, given the optimal wealth and consumption processes. A special attention is paid to utilities associated with linear optimal processes with respect to their initial conditions, which is for example the case of power progressive utilities. Those utilities are the basis point to construct other progressive utilities generating non linear optimal processes but leading yet to still tractable computations. This is of particular interest to study the impact of initial wealth on yield curves.
The purpose of this paper relies on the study of long term yield curves modeling. Inspired by the economic litterature, it provides a financial interpretation of the Ramsey rule that links discount rate and marginal utility of aggregate optimal consu
This paper proposes a paradigm shift in the valuation of long term annuities, away from classical no-arbitrage valuation towards valuation under the real world probability measure. Furthermore, we apply this valuation method to two examples of annuit
A New Trinomial Recombination Tree Algorithm and Its Applications
In this paper we propose two efficient techniques which allow one to compute the price of American basket options. In particular, we consider a basket of assets that follow a multi-dimensional Black-Scholes dynamics. The proposed techniques, called G
This paper proposes the sample path generation method for the stochastic volatility version of CGMY process. We present the Monte-Carlo method for European and American option pricing with the sample path generation and calibrate model parameters to