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Early real business-cycle models postulated an economy populated by a representative consumer who operates in perfectly competitive markets. The only sources of uncertainty in these models are "shocks" in technology. [2] RBC theory builds on the neoclassical growth model, under the assumption of flexible prices, to study how real shocks to the ...
Merton's portfolio problem is a problem in continuous-time finance and in particular intertemporal portfolio choice.An investor must choose how much to consume and must allocate their wealth between stocks and a risk-free asset so as to maximize expected utility.
Geometric Brownian motion is used to model stock prices in the Black–Scholes model and is the most widely used model of stock price behavior. [4] Some of the arguments for using GBM to model stock prices are: The expected returns of GBM are independent of the value of the process (stock price), which agrees with what we would expect in ...
The Brownian motion models for financial markets are based on the work of Robert C. Merton and Paul A. Samuelson, as extensions to the one-period market models of Harold Markowitz and William F. Sharpe, and are concerned with defining the concepts of financial assets and markets, portfolios, gains and wealth in terms of continuous-time stochastic processes.
The consistency of the accounting is ensured by the use of three matrices: i) the aggregate balance sheets, with all the initial stocks, ii) the transaction flow, recording all the transactions taking places in the economy (e.g. consumption, interests payments); iii) the stock revaluation matrix, showing the changes in the stocks resulting from ...
Proposed by economist Stephen Ross in 1976, [1] it is widely believed to be an improved alternative to its predecessor, the capital asset pricing model (CAPM). [2] APT is founded upon the law of one price, which suggests that within an equilibrium market, rational investors will implement arbitrage such that the equilibrium price is eventually ...
For any cadlag process Y t, the left limit in t is denoted by Y t−, which is a left-continuous process. The jumps are written as ΔY t = Y t − Y t−. Then, Itô's lemma states that if X = (X 1, X 2, ..., X d) is a d-dimensional semimartingale and f is a twice continuously differentiable real valued function on R d then f(X) is a ...
The trinomial tree is a lattice-based computational model used in financial mathematics to price options. It was developed by Phelim Boyle in 1986. It is an extension of the binomial options pricing model, and is conceptually similar. It can also be shown that the approach is equivalent to the explicit finite difference method for option ...