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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.
In financial mathematics, no-arbitrage bounds are mathematical relationships specifying limits on financial portfolio prices. These price bounds are a specific example of good–deal bounds, and are in fact the greatest extremes for good–deal bounds. [1] The most frequent nontrivial example of no-arbitrage bounds is put–call parity for ...
2.1 Mathematics. 2.2 Physics. ... This is a list of equations, ... Price equation; Economics. Black–Scholes equation; Fisher equation
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 ...
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 ...
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 ...
Under the trinomial method, the underlying stock price is modeled as a recombining tree, where, at each node the price has three possible paths: an up, down and stable or middle path. [2] These values are found by multiplying the value at the current node by the appropriate factor u {\displaystyle u\,} , d {\displaystyle d\,} or m ...