Certain Merton type consumption−investment problems under partial information are reduced to the ones of full and within framework a complete market model. Then, specializing conditionally log−Gaussian diffusion models, concrete analysis about optimal values strategies is performed by using analytical tools like Feynman−Kac formula, or HJB equations. The explicit solutions related forward-backw...

We show how to solve Merton optimal investment stochastic control problem for Hawkes-based models in finance and insurance, i.e., a wealth portfolio X(t) consisting of bond stock price described by general compound Hawkes process (GCHP), capital R(t) an insurance company with the amount claims risk model based on GCHP. The novelty results consists new those models.

We analyze the joint convergence of sequences of discounted stock prices and Radon-Nicodym derivatives of the minimal martingale measure when interest rates are stochastic. Therefrom we deduce the convergence of option values in either complete or incomplete markets. We illustrate the general result by two main examples: a discrete time i.i.d. approximation of a Merton type pricing model for op...

Robert K. Merton and Elinor Barber’s The Travels and Adventures of Serendipity (Englishlanguage translation 2004) is the history of a word and its related concept. The choice of writing a book about a word may surprise those who are not acquainted with Merton’s work, but certainly not those sociologists that have chosen him as a master. Searching, defining, and formulating concepts has always b...

Modern option pricing techniques are often considered among the most mathematically complex of all applied areas of financial engineering. In particular these techniques derive their impetus from four milestones of option pricing models: Bachelier model, Samuelson model, Black-Scholes-Merton model and Levy model. In this paper we evaluate all related option pricing models based on these milesto...

On the Pricing of Corporate Debt: The Risk Structure of Interest Rates Author(s): Robert C. Merton Source: The Journal of Finance, Vol. 29, No. 2, Papers and Proceedings of the Thirty-Second Annual Meeting of the American Finance Association, New York, New York, December 28-30, 1973 (May, 1974), pp. 449-470 Published by: Blackwell Publishing for the American Finance Association Stable URL: http...

We address the optimal consumption-investment-retirement problem considering stochastic labor income. We study the Merton problem assuming that the agent has to take four different decisions: the retirement date which is irreversible; the labor and the consumption rate and the portfolio decision before retirement. After retirement the agent only chooses the portfolio and the consumption rate. W...

Using the symmetry group that was found in [1] and further studied in [2], in this work we study the partial differential equation of the Black-Scholes model [3] and relate such symmetries with the Mellin transform to find the price of an european like investment option. We also consider the Black-Schoes-Merton equation in the non-linear case that models investments in which volatility is a fun...

We present a solution to an optimal stopping game for geometric Brownian motion with gain functions having the form of payoff functions of spread options. The method of proof is based on reducing the initial problem to a free-boundary problem and solving the latter by means of the smooth-fit principle. The derived result can be interpreted as pricing the (perpetual) spread game option in the Bl...

In this paper we solve the problem of determining the default time of a firm in such a way as to maximize its total value, which includes bankruptcy costs and tax benefits, with the condition that the value of equity must be nonnegative. By applying dynamic programming in discrete time, we find results which extends those of Merton (1974), and we give an application for the approximation of mod...