# Stochastic Modeling in Economics and Finance (Applied Optimization)

# Stochastic Modeling in Economics and Finance (Applied Optimization)

Language: English

Pages: 386

ISBN: 1441952314

Format: PDF / Kindle (mobi) / ePub

In Part I, the fundamentals of financial thinking and elementary mathematical methods of finance are presented. The method of presentation is simple enough to bridge the elements of financial arithmetic and complex models of financial math developed in the later parts. It covers characteristics of cash flows, yield curves, and valuation of securities.

Part II is devoted to the allocation of funds and risk management: classics (Markowitz theory of portfolio), capital asset pricing model, arbitrage pricing theory, asset & liability management, value at risk. The method explanation takes into account the computational aspects.

Part III explains modeling aspects of multistage stochastic programming on a relatively accessible level. It includes a survey of existing software, links to parametric, multiobjective and dynamic programming, and to probability and statistics. It focuses on scenario-based problems with the problems of scenario generation and output analysis discussed in detail and illustrated within a case study.

Sliding Mode Control and Observation (Control Engineering)

MEI A2 Further Pure Mathematics FP2 (3rd Edition)

Love and Math: The Heart of Hidden Reality

Puzzling Adventures: Tales of Strategy, Logic and Mathematical Skill

obtain a new estimate of speci- We must take the diagonal only since may not be a diagonal matrix. We go back to (15), form the new reduced correlation matrix and iteratively improve the estimates of and B until the differences in successive iterations are sufficiently small. Eventually we get the decomposition or an analogy to the original model (8) with f still remaining an unknown vector of common factors. But with known matrix we may look on (19) as on a linear regression model with unknown

takes into account the remaining stages Finally, one may reformulate the problem into the form of a stochastic dynamic program and solve it by the backward recursion; see Example 2.5.1. II. DISCRETE TIME STOCHASTIC DECISION MODELS 119 2.4.1 Exercise. (i) Modify the flower-girl problem to include unit carry-over costs q! (ii) Rewrite the 3-stage flower-girl problem as a sequence of nested two-stage programs. Observe that the third stage program has an optimal solution This means that the

(7) and solve it. Another possibility is to use the form (2), (3), (12) whose set of feasible solutions is not influenced by inclusion of additional scenarios. The additional scenarios appear only in the objective function which is an expected value of the utility of the final wealth under a discrete probability distribution carried by a finite number of scenarios. Being an expected value, the objective function (12) is linear in the probability distribution. Denote by P the initial probability

(7) and solve it. Another possibility is to use the form (2), (3), (12) whose set of feasible solutions is not influenced by inclusion of additional scenarios. The additional scenarios appear only in the objective function which is an expected value of the utility of the final wealth under a discrete probability distribution carried by a finite number of scenarios. Being an expected value, the objective function (12) is linear in the probability distribution. Denote by P the initial probability

government bonds (without option) characterized by their maturities the postulated model is where the random errors are independent, normal There is a good reason to accept the hypothesis of approximately normal errors in (17) which is in line with the assumed log-normal process of short rates approximated by the Black-Derman-Toy binomial lattice. The yield curve for September 1, 1994 estimated according to the linearized Bradley and Crane model (12) is plotted on Figure 8. Naturally, the fit is