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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 .
The Merton model, [1] developed by Robert C. Merton in 1974, is a widely used "structural" credit risk model. Analysts and investors utilize the Merton model to understand how capable a company is at meeting financial obligations, servicing its debt, and weighing the general possibility that it will go into credit default.
where is the maturity of the longest transaction in the portfolio, is the future value of one unit of the base currency invested today at the prevailing interest rate for maturity , is the loss given default, is the time of default, () is the exposure at time , and (,) is the risk neutral probability of counterparty default between times and .
The magnitude of the equity premium brings about substantial implications for policy, welfare and also resource allocation. Policy and Welfare Implications. Campbell and Cochrane (1995) have found in a study of a model that simulates equity premium value's consistent with asset prices, welfare costs are similar in magnitude to welfare benefits ...
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.
In finance, the Monte Carlo method is used to simulate the various sources of uncertainty that affect the value of the instrument, portfolio or investment in question, and to then calculate a representative value given these possible values of the underlying inputs. [1] ("Covering all conceivable real world contingencies in proportion to their ...
An estimation of the CAPM and the security market line (purple) for the Dow Jones Industrial Average over 3 years for monthly data.. In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversified portfolio.
The monetary value of each asset may influence the risk/reward ratio of the portfolio. When determining asset allocation, the aim is to maximise the expected return and minimise the risk. This is an example of a multi-objective optimization problem : many efficient solutions are available and the preferred solution must be selected by ...