Brownian Motion and Stochastic Calculus

Abstract

I TAKEUTIIZARING . Introduction to Axiomatic Set Theory. 2nd ed . OXTOBY . Measure and Category. 2nd ed . SCHAEFFER. Topological Vector Spaces . HILTON/STAMMBACH . A Course in Hom ological Algebra. MACLANE. Categories for the Working Mathematician. HUGHES/PIPER . Projective Planes . SERRE. A Course in Arithmetic . TAKEUTI/ZARING . Axiomatic Set Theory . HUMPHREYS . Introduction to Lie Algebras and Representation Theory. COHEN . A Course in Simple Homotopy Theory. II CONWAY . Functions of One Complex Variable . 2nd ed . BEALS . Advanced Mathematical Analysis. ANDERSON/FuLLER . Rings and Categories of Modules . GOLUBITSKy/GUILLEMIN . Stable Mappings and Their Singularities . BERBERIAN . Lectures in Functional Analysis and Operator Theory. WINTER. The Structure of Fields. ROSENBLATT. Random Processes . 2nd ed . HALMos. Measure Theory . HALMos. A Hilbert Space Problem Book. 2nd ed . • revi sed . HUSEMOLLER . Fibre Bundles . 2nd ed . HUMPHREYS. Linear Algebraic Groups . BARNES/MACK . An Algebraic Introduction to Mathematical Logic . GREUB . Linear Algebra. 4th ed . HOLMES . Geometric Functional Analysis and its Applications . HEWITT/STROMBERG . Real and Abstract Analysis. MANES. Algebraic Theories. KELLEY . General Topology.

No arbitrage conditions for simple trading strategies

“…[5]. CEV models are regular strong Markov processes: for the case ρ > 1 this is stated in [8], on the other hand for ρ ∈ (0, 1) this fact follows from Sections 5.4 and 5.5 of [10] (since the conditions ND' and LI' on p 343 hold). Finally observe that ρ = 1 is the classical geometric Brownian motion model.…”

Optimal Consumption and Portfolio Selection with Stochastic Differential Utility

“…The meaning will always be clear from the context. Restrictions on + Y and _ Y that guarantee C5(a) are well known and can be found, for example, in Karatzas and Shreve [32]. In the case in which r and ' are deterministic processes, the process Y should be taken to be the empty function.…”

Smiles All Around: FX Joint Calibration in a Multi-Heston Model

“…The Laplace transform G solves the following backward Kolmogorov equation Karatzas and Shreve (1991):…”