Asset Pricing Theory is an advanced textbook for doctoral students and researchers that offers a modern introduction to the theoretical and methodological foundations of competitive asset pricing. Costis Skiadas develops in depth the fundamentals of arbitrage pricing, mean-variance analysis, equilibrium pricing, and optimal consumption/portfolio choice in discrete settings, but with emphasis on geometric and martingale methods that facilitate an effortless transition to the more advanced continuous-time theory. Among the book's many innovations are its use of recursive utility as the benchmark representation of dynamic preferences, and an associated theory of equilibrium pricing and optimal portfolio choice that goes beyond the existing literature. Asset Pricing Theory is complete with extensive exercises at the end of every chapter and comprehensive mathematical appendixes, making this book a self-contained resource for graduate students and academic researchers, as well as mathematically sophisticated practitioners seeking a deeper understanding of concepts and methods on which practical models are built.
Covers in depth the modern theoretical foundations of competitive asset pricing and consumption/portfolio choice
Uses recursive utility as the benchmark preference representation in dynamic settings
Sets the foundations for advanced modeling using geometric arguments and martingale methodology
Features self-contained mathematical appendixes
Includes extensive end-of-chapter exercises
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AGENTS TRADE in financial markets in order to transfer funds across time and states of nature. Transfers across time correspond to saving or borrowing. Transfers across states of nature correspond to hedging or speculation. This chapter introduces a simple and highly idealized model that captures this basic function of financial markets and will also serve as a building block in the dynamic extension of Part II. Within this simple model, we develop the foundations of arbitrage-pricing theory. The mathematical background for Chapters 1 and 2 is contained in the first seven sections of Appendix A.
1.1 MARKET AND ARBITRAGE
There are two times, labeled zero and one. At time zero there is no uncertainty, while at time one there are K possible states that can prevail, labeled 1, 2, . . . , K. We treat time zero and each of the K states in an integrated fashion and we refer to them as spots. There are therefore 1 + K spots, labeled 0, 1, . . . , K.
A cash flow is a vector of the form
. Alternatively, a cash flow c can be thought of as the stochastic process (c(0), c(1)), where c(0) = c0 and
is a random variable taking the value c(1)k = ck at state k. We assume that each ck is real-valued, representing a spot-contingent payment in some unit of account. We regard the set of cash flows as an inner-product space with the usual Euclidean inner product:
The Arrow cash flow corresponding to spot k is denoted 1k and is defined by
In particular, 10 = (1, 0, . . . , 0). The Arrow cash flows correspond to the usual Euclidean basis of
and therefore every cash flow is a linear combination of Arrow cash flows.
A financial market can be thought of as a set X of net incremental cash flows that can be obtained by trading financial contracts such as bonds, stocks, futures, options and swaps. In this text, we consider perfectly competitive markets, that is, markets in which every trader has negligible market power and therefore takes the terms and prices of contracts as given. Unless otherwise indicated, we also assume that there are no position limits or short sale constraints, there are no transaction costs such as bid-ask spreads and no indivisibilities such as minimum amounts that one can trade in any one contract.
The above informal assumptions motivate the following formal properties of the set of traded cash flows X:
