Risk-Neutral Valuation
Pricing and Hedging of Financial Derivatives
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12 Result(s)
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Rüdiger Kiesel
Probability Theory and Stochastic Processes
Quantitative Finance
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Book
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Chapter
The Separating Hyperplane Theorem
In a vector space V, if x and y are vectors, the set of linear combinations αx + αy, with scalars α, β ≥ 0 with sum α + β = 1, represents geometrically the linesegment joining x to y. Each such linear combination...
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Chapter
Projections and Conditional Expectations
Given a Hilbert space (or more generally, an inner product space) V, suppose V is the direct sum of a closed subspace M and its orthogonal complement MΓ: ...
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Chapter
Stochastic Processes in Discrete Time
Access to full, accurate, up-to-date information is clearly essential to anyone actively engaged in financial activity or trading. Indeed, information is arguably the most important determinant of success in f...
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Chapter
Incomplete Markets
We now return to general continuous-time financial market models in the setting of §6.1, i.e. there are d+1 primary traded assets whose price processes are given by stochastic processes S 0,... , S ...
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Chapter
Hilbert Space
Recall our use of n-dimensional Euclidean space ℝ n , the set of n-vectors or n-tuples x = (x 1,... ,x n ) with each x ...
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Chapter
Probability Background
No-one can predict the future! All that can be done by way of prediction is to use what information is available as well as possible. Our task is to make the best quantitative statements we can about uncertain...
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Chapter
Mathematical Finance in Discrete Time
We will study so-called finite markets — i.e. discrete-time models of financial markets in which all relevant quantities take a finite number of values. Following the approach of Harrison and Pliska [115] and ...
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Chapter
Mathematical Finance in Continuous Time
This chapter discusses the general principles of continuous-time financial market models. In the first section we use a rather general model, which will serve also as a reference in the later chapters. A thoro...
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Chapter
Interest Rate Theory
In this chapter we apply the techniques developed in the previous chapters to the fast-growing fixed-income securities market. We mainly focus on the continuous-time model (since the available tools from stoch...
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Chapter
Derivative Background
The main focus of this book is the pricing of financial assets. Price formation in financial markets may be explained in an absolute manner in terms of fundamentals, as, e.g. in the so-called rational expectat...
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Chapter
Stochastic Processes in Continuous Time
The underlying set-up is as in Chapter 3: we need a complete probability space (Ω, ℱ, ℙ), equipped with a filtration, i.e a nondecreasing family F = (F t ) ...
