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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

Inspired by the Monty Hall Problem and a popular simple solution to it, we present a number of game-show puzzles that are analogous to the notorious Sleeping Beauty Problem (and variations on it), but much easier to solve. We replace the awakenings of Sleeping Beauty by contestants on a game show, like Monty Hall’s, and increase the number of awakenings/contestants in the same way that the number of doors in the Monty Hall Problem is increased to make it easier to see what the solution to the problem is. We show that these game-show proxies for the Sleeping Beauty Problem and variations on it can be solved through simple applications of Bayes’s theorem. This means that we will phrase our analysis in terms of credences or degrees of belief. We will also rephrase our analysis, however, in terms of relative frequencies. Overall, our paper is intended to showcase, in a simple yet non-trivial example, the efficacy of a tried-and-true strategy for addressing problems in philosophy of science, i.e., develop a simple model for the problem and vary its parameters. Given that the Sleeping Beauty Problem, much more so than the Monty Hall Problem, challenges the intuitions about probabilities of many when they first encounter it, the application of this strategy to this conundrum, we believe, is pedagogically useful. Full article

This paper formulates the classic Monty Hall problem as a Bayesian game. Allowing Monty a small amount of freedom in his decisions facilitates a variety of solutions. The solution concept used is the Bayes Nash Equilibrium (BNE), and the set of BNE relies on Monty’s motives and incentives. We endow Monty and the contestant with common prior probabilities (p) about the motives of Monty and show that, under certain conditions on p, the unique equilibrium is one in which the contestant is indifferent between switching and not switching. This coincides and agrees with the typical responses and explanations by experimental subjects. In particular, we show that our formulation can explain the experimental results in Page (1998), that more people gradually choose switch as the number of doors in the problem increases. Full article