Search Results (4)

Forecast risk management is central to the financial management process. This study aims to apply Monte Carlo simulation to solve three classic probabilistic paradoxes and discuss their implementation in corporate financial management. The article presents Monte Carlo simulation as an advanced tool for risk management in financial management processes. This method allows for a comprehensive risk analysis of financial forecasts, making it possible to assess potential errors in cash flow forecasts and predict the value of corporate treasury growth under various future scenarios. In the investment decision-making process, Monte Carlo simulation supports the evaluation of the effectiveness of financial projects by calculating the expected net value and identifying the risks associated with investments, allowing more informed decisions to be made in project implementation. The method is used in reducing cash flow volatility, which contributes to lowering the cost of capital and increasing the value of a company. Simulation also enables more accurate liquidity planning, including forecasting cash availability and determining appropriate financial reserves based on probability distributions. Monte Carlo also supports the management of credit and interest rate risk, enabling the simulation of the impact of various economic scenarios on a company’s financial obligations. In the context of strategic planning, the method is an extension of decision tree analysis, where subsequent decisions are made based on the results of earlier ones. Creating probabilistic models based on Monte Carlo simulations makes it possible to take into account random variables and their impact on key financial management indicators, such as free cash flow (FCF). Compared to traditional methods, Monte Carlo simulation offers a more detailed and precise approach to risk analysis and decision-making, providing companies with vital information for financial management under uncertainty. This article emphasizes that the use of Monte Carlo simulation in financial management not only enhances the effectiveness of risk management, but also supports the long-term growth of corporate value. The entire process of financial management is able to move into the future based on predicting future free cash flows discounted at the cost of capital. We used both numerical and analytical methods to solve veridical paradoxes. Veridical paradoxes are a type of paradox in which the result of the analysis is counterintuitive, but turns out to be true after careful examination. This means that although the initial reasoning may lead to a wrong conclusion, a correct mathematical or logical analysis confirms the correctness of the results. An example is Monty Hall’s problem, where the intuitive answer suggests an equal probability of success, while probabilistic analysis shows that changing the decision increases the chances of winning. We used Monte Carlo simulation as the numerical method. The following analytical methods were used: conditional probability, Bayes’ rule and Bayes’ rule with multiple conditions. We solved truth-type paradoxes and discovered why the Monty Hall problem was so widely discussed in the 1990s. We differentiated Monty Hall problems using different numbers of doors and prizes. Full article

We give two new ways of calculating the probability of a chord of circumference randomly selected being larger than the side of an equilateral triangle inscribed in the circumference (this problem is known as the Bertrand paradox). The first one employs an immersion in R⁴, and the second one uses a direct probability measure over the set of chords. Full article

The Principle of Indifference (‘PI’: the simplest non-informative prior in Bayesian probability) has been shown to lead to paradoxes since Bertrand (1889). Von Mises (1928) introduced the ‘Wine/Water Paradox’ as a resonant example of a ‘Bertrand paradox’, which has been presented as demonstrating that the PI must be rejected. We now resolve these paradoxes using a Maximum Entropy (MaxEnt) treatment of the PI that also includes information provided by Benford’s ‘Law of Anomalous Numbers’ (1938). We show that the PI should be understood to represent a family of informationally identical MaxEnt solutions, each solution being identified with its own explicitly justified boundary condition. In particular, our solution to the Wine/Water Paradox exploits Benford’s Law to construct a non-uniform distribution representing the universal constraint of scale invariance, which is a physical consequence of the Second Law of Thermodynamics. Full article

Bertrand’s paradox is a problem in geometric probability that has resisted resolution for more than one hundred years. Bertrand provided three seemingly reasonable solutions to his problem — hence the paradox. Bertrand’s paradox has also been influential in philosophical debates about frequentist versus Bayesian approaches to statistical inference. In this paper, the paradox is resolved (1) by the clarification of the primary variate upon which the principle of maximum entropy is employed and (2) by imposing constraints, based on a mathematical analysis, on the random process for any subsequent nonlinear transformation to a secondary variable. These steps result in a unique solution to Bertrand’s problem, and this solution differs from the classic answers that Bertrand proposed. It is shown that the solutions proposed by Bertrand and others reflected sampling processes that are not purely random. It is also shown that the same two steps result in the resolution of the Bing–Fisher problem, which has to do with the selection of a consistent prior for Bayesian inference. The resolution of Bertrand’s paradox and the Bing–Fisher problem rebuts philosophical arguments against the Bayesian approach to statistical inference, which were based on those two ostensible problems. Full article