In his 1922 review for Cambridge Magazine of Keynes's A Treatise on Probability, and again in his 1926 review "Truth and Probability" (published in 1931 and republished in Kyburg and Smokler's 1980 edition), Ramsey provided examples critiquing Keynes's logical theory of probability. However, these examples do not disprove Keynes's theory as all of them are flawed. The flaws arise because all the pairs of propositions that Ramsey used to substantiate his criticisms are irrelevant to each other. Such irrelevant propositions are explicitly excluded from Keynes's theory in pages 4-6 of his A Treatise on Probability. This paper highlights that Ramsey's examples, which involve irrelevant propositions, do not disprove Keynes's Boolean, relational logic. The only other defense of Keynes's theory, put forth by Watt in 1989, was found to be deficient by Brady in 2022.

Liquidity can be a real phenomenon for execution of the financial holding. Its risk falls in debate to impose a conditional cost on the counterparty. The time-varying liquidity is often linked to the expected fundamental value of an investment. In this work, the microblogging-based informed transaction is examined as a determinant of the liquidity-facilitating cost. Most importantly, this study investigates the economic blockade era and post-pandemic uncertainty. The sentiment indicators were found to be determinants of liquidity. These findings were consistent in the post-pandemic period. However, the investor pessimistic sentiment was a priced risk factor in liquidity during the economic blockade period. Based on the Bayesian theorem, a relativeness was reported between sentiment indicators and the liquidity-facilitating cost. The same findings were depicted in environments of the pandemic era. Nevertheless, the posterior probability indicated an occurrence of the liquidity-associated cost in response to the pessimistic sentiments during the economic blockade period. This quantification may have potential implications in terms of exploring liquidity from the microblogging perceptive.

Calculating the amount of regulatory capital to cover unexpected losses due to operational events in the upcoming year has caused problems because of difficulties in fitting probability distributions to data. It is consequently difficult to judge an appropriate level of capital that reflects the risk profile of a financial institution. We provide theoretical and empirical analyses to link the calculated capital to the sum of losses using appropriate statistical approximations. We conclude that, in order to reasonably reflect the associated risk, the capital should be approximately half the sum of losses, with a wide bound for the ratio of capital to sum.

This study aims to examine the effects of student loan debt on the decisions of U.S. married households to invest in stocks located in non-retirement accounts. Using longitudinal datasets from the 2011 to 2017 U.S. Panel Study of Income Dynamics and a fixed effects logit model, the results show mixed findings. The presence of student debt decreases the probability that married households will own stocks, but the amount of student debt does not show a statistically significant effect. The findings suggest that the incidence of student debt raises the perception of liquidity constraints and debt burden among married households.

We quantify financial returns to backers in reward-based crowdfunding projects on Kickstarter and show that such investments provide profitable opportunities in addition to non-monetary benefits. The average unconditional annualized return is 11.5% and the average return on successful projects is 30%. Hence, backing money near the end of a campaign, when the probability of success is already high, is a profitable strategy. The most attractive is the Design category, where successful projects yield 73%, on average. Short-term projects are more profitable than long-term ones. Financial return is an important type of extrinsic motivation in reward-based crowdfunding, which has generally been neglected in academic literature. Reward-based crowdfunding outperforms other forms of crowdfunding and other common alternative investments.

In the behavioral domain, this study discloses the pattern between microblogging-opinionated information and yields on the investment. This phenomenon is particularly related to the political instability in the Pakistan’s economy through the multivariate techniques. Pre-political crisis, the pessimistic sentiments were priced in yields on the investment. In environments of political instability, the intensity of decline in yields was more responsive against an incline in the negative opinions. Meanwhile, the intensity of increase in returns was less responsive against an incline in the positive opinions. The findings were further supported by the Bayesian approach. Before the political instability takes place in the Pakistan’s economy, the occurrence of yields was noted in response to the bearish market period. Post-political instability, there was a higher posterior probability for occurrence of returns against the bearish market period. Conversely, a higher posterior likelihood was noted for occurrence of investment’s yields in response to the bullish market period, but this relevance was not completely probable. From the impulse response analysis, the response of returns was reported against the standard deviation shocks in the microblogging sentiment indicators. The analysis may have potential implications in terms of disclosing the investors’ behavior from a political perspective.

In this study, the time-varying pattern of returns with the trading cost is assessed in light of sanctions on the Russia’s economy. The analysis is performed on the Moscow Exchange Index (MOEX) using the ordinary least squares (OLS) method, Bayes’ Theorem technique, and vector error correction model (VECM). Firstly, the transparency of asset’s value in the same trading period was noted to execute the trade with a limited price impact. Thus, the liquidity seems not priced in returns. In addition, the posterior probability of the transparent asset’s value stabilized the market at a limited transaction cost. In this case, there is less likelihood of liquidity acting as a risk element in returns during the same trading session. These results correspond to the era without sanctions, as well as economic restrictions period. Before the economic restrictions, the execution of investment occurred on its real or close value due to the market transparency in the following trading period. This implies, that the past trading cost series is not priced in yields on investment. During the Russia-related sanctions, a higher price impact of transaction was noted due to the ambiguity in the future asset’s value. Therefore, the past liquidity series is a pricing element in the short run and long run. The analysis suggests a potential inference of trading cost to determine the yield on investment.