Showing papers on "Mathematical finance published in 1990"

A change of variables formula for stratonovich integrals and existence of solutions for two-point stochastic boundary value problems

Abstract: Existence results for a class of two point non-adaptive stochastic boundary value problems are derived by combining a (new) change of variables formula with optimal control techniques. The class of equations treated is significantly wider than that for which previously known existence results apply.

Harmonizability,V-boundedness, (2,p)-boundedness of stochastic processes

Abstract: Some new classes of discrete time non-stationary processes, related to the harmonizable andV-bounded classes, are introduced. A few characterizations are obtained which, in turn, unify theV-bounded theory. Our main results depend on a special form of Grothendieck's inequality.

Regularity, partial regularity, partial information process, for a filtered statistical model

Abstract: We define “partial regularity” for a filtered statistical (semi-parametric) model indexed by θ∈ℝd, as differentiability in a suitable sense of the partial likelihoods associated with a basic processX. Partial regularity turns out to be equivalent to some sort of differentiability in θ of the characteristics ofX. We also prove that regularity of the model implies partial regularity, and we define a “partial information process”, which is smaller than the “complete” information process. We apply these results to obtain a generalization of Cramer-Rao inequality, and to prove that partial likelihood processes are optimal among all quasi-likelihood processes which are stochastic integrals with respect to the basic processX.

On the probable maximum loss

Abstract: In some nonlife insurance branches the probable maximum loss is of great importance for judging a given risk or a given collective of risks. In the present paper, the author gives a general mathematical definition and a new practicable calculation method for the probable maximum loss.

Strong laws and limit theorems for local time of Markov processes

Abstract: The local time of a Markov process can be constructed from the length of small excursions. We obtain the exact almost sure rate of this construction. We also prove a functional limit theorem for the difference between the length of small excursions and the local time at zero.

East India Bonds, 1718-1763 Exotic Derivatives, Efficiency, and the Financial Revolution

Abstract: Were 18 th century financial markets efficient? Neal (1990) shows that the London and Amsterdam markets were integrated. Yet some scholars find that the London capital market was either not integrated across various classes of securities, or was comprised of ignorant investors who were not knowledgeable enough to arbitrage across securities with different maturities, or was even irrational at times. In this paper, we demonstrate that this misunderstanding arises from an incorrect comprehension of the pricing of the financial instrument they use. After examining certain features peculiar to India bonds overlooked by previous authors, we make it clear not only that 18 th century investors were already proficient in international arbitraging, as Neal indicates, but also that they were capable of handling sophisticated options, well before the rise of modern financial mathematics and Black and Scholes’ (1973) contribution to options theory.

Practical exponential smoothing credibility

Abstract: Since some time so-called credibility estimators with geometric weights are of some practical importance. As alternatives one can use so-called exponential smoothing credibility estimators. In the present paper the second ones are prepared for practical application.

11 – Option Pricing and Stochastic Processes

Abstract: Publisher Summary Stochastic processes and the theory of stochastic differential equations have played a fundamental role in the theory of option pricing. An option gives the holder or owner of it the right to buy or sell something at his discretion before a certain prescribed date at a price specified in advance. Black and Scholes were the first who derived the equilibrium price of an option which gives the owner the right to buy a stock before a certain date at a fixed price. They used a stochastic process to model the price of the stock. The theory of stochastic differential equations had been developed to obtain a direct solution of the partial differential equation in terms of the expected value of a certain stochastic variable, without any reference to physics. The so-called Kolmogorov-backward equation gives the direct solution. The formula of Black and Scholes is not only widely accepted by academic theorists but also used as a black-box by market participants to calculate prices for options they want to sell or buy. But the Black–Scholes formula cannot be used to explain price behavior for all kinds of options. Stochastic differential equations are not only used to price options but are also applied in a more general way to describe optimal consumption and investment decisions in a continuous-time setting.

Quantitative Methods for Business Students

Abstract: Provides a revision of basic mathematical topics and covers all the common tools of business mathematics, including matrices, differential and integral calculus, inequalities and linear programmimg and financial mathematics.