Bounded Risk Two-stage Estimation Procedure for a U(aq, bq) Distribution

In the literature, an extensive work on sequential fixed-width confidence interval for the parameter of U( q, m q) model, where m > 1 is known, is available. In this article, we propose a two-stage sampling procedure for estimating the parameter q of U( aq, bq) distribution, where a < b are positive and known. Here, the risk of an estimator [Formula: see text] of q is less than a pre-assigned number w (>0), that is, [Formula: see text], 0 < A < ∞ is known. We determine the parameter Bk of stopping variable so that the risk is uniformly bounded by a pre-assigned value w. We have also tabulated the values of the expected stopping time and its standard deviation (SD).

Investing with Cryptocurrencies—a Liquidity Constrained Investment Approach*

Cryptocurrencies have left the dark side of the finance universe and become an object of study for asset and portfolio management. Since they have low liquidity compared to traditional assets, one needs to take into account liquidity issues when adding them to a portfolio. We propose a Liquidity Bounded Risk-return Optimization (LIBRO) approach, which is a combination of risk-return portfolio optimization under liquidity constraints. Cryptocurrencies are included in portfolios formed with stocks of the S&P 100, US Bonds, and commodities. We illustrate the importance of the liquidity constraints in an in-sample and out-of-sample study. LIBRO improves the weight optimization in the sense that it only adds cryptocurrencies in tradable amounts depending on the intended investment amount. The returns greatly increase compared to portfolios consisting only of traditional assets. We show that including cryptocurrencies in a portfolio can indeed improve its risk–return trade-off.

DETERMINISTIC CRITERIA FOR THE ABSENCE AND EXISTENCE OF ARBITRAGE IN MULTI-DIMENSIONAL DIFFUSION MARKETS

We derive deterministic criteria for the existence and nonexistence of equivalent (local) martingale measures for financial markets driven by multi-dimensional time-inhomogeneous diffusions. Our conditions can be used to construct financial markets in which the no unbounded profit with bounded risk condition holds, while the classical no free lunch with vanishing risk condition fails.