An analysis of acceptance policies for blockchain transactions

The standard acceptance policy for a cryptocurrency transaction at most exchanges is to wait until the transaction is placed in the blockchain and followed by a certain number of blocks. However, as noted by Sompolinsky and Zohar [16], the amount of time for blocks to arrive should also be taken into account as it affects the probability of double spending. Specifically, they propose a dynamic policy for transaction acceptance that depends on both the number of confirmations and the amount of time since transaction broadcast. In this work we study the implications of using such a policy compared with the standard option that ignores block timing information. Using an exact expression for the probability of double spend, via numerical results, we analyze time to transaction acceptance (performance) as well as the time and cost to perform a double spend attack (security). We show that while expected time required for transaction acceptance is improved using a dynamic policy, the time and cost to perform a double spend attack for a particular transaction is reduced.First author draf

Continuous-Time Markowitz's Model with Transaction Costs

A continuous-time Markowitz's mean-variance portfolio selection problem is studied in a market with one stock, one bond, and proportional transaction costs. This is a singular stochastic control problem,inherently in a finite time horizon. With a series of transformations, the problem is turned into a so-called double obstacle problem, a well studied problem in physics and partial differential equation literature, featuring two time-varying free boundaries. The two boundaries, which define the buy, sell, and no-trade regions, are proved to be smooth in time. This in turn characterizes the optimal strategy, via a Skorokhod problem, as one that tries to keep a certain adjusted bond-stock position within the no-trade region. Several features of the optimal strategy are revealed that are remarkably different from its no-transaction-cost counterpart. It is shown that there exists a critical length in time, which is dependent on the stock excess return as well as the transaction fees but independent of the investment target and the stock volatility, so that an expected terminal return may not be achievable if the planning horizon is shorter than that critical length (while in the absence of transaction costs any expected return can be reached in an arbitrary period of time). It is further demonstrated that anyone following the optimal strategy should not buy the stock beyond the point when the time to maturity is shorter than the aforementioned critical length. Moreover, the investor would be less likely to buy the stock and more likely to sell the stock when the maturity date is getting closer. These features, while consistent with the widely accepted investment wisdom, suggest that the planning horizon is an integral part of the investment opportunities.Comment: 30 pages, 1 figur

Finite Horizon Portfolio Selection

We study the problem of maximising expected utility of terminal wealth over a nite horizon, with one risky and one riskless asset available, and with trades in the risky asset subject to proportional transaction costs. In a discrete time setting, using a utility function with hyperbolic risk aversion, we prove that the optimal trading strategy is characterised by a function of time (t), which represents the ratio of wealth held in the risky asset to that held in the riskless asset. There is a time varying no transaction region with boundaries b(t) < s(t), such that the portfo- lio is only rebalanced when (t) is outside this region. The results are consistent with similar studies of the in nite horizon problem with in- termediate consumption, where the no transaction region has a similar, but time independent, characterisation. We solve the problem numerically and compute the boundaries of the no transaction region for typical model parameters. We show how the results can be used to implement option pricing models with transaction costs based on utility maximisation over a nite horizo

The transition from national currencies to the Euro.

We initiated a survey to examine whether the transition from national currencies to the Euro involved significant increases in transaction times. Based on our sample of 42 observations, we found that the pure transaction time for making change did actually increase, while queuing time increased only in small shops. This increase in transaction time represented a more significant welfare loss than most estimated studies of shoe-leather cost have previously found.

Optimal Investment with Transaction Costs and Stochastic Volatility

Two major financial market complexities are transaction costs and uncertain volatility, and we analyze their joint impact on the problem of portfolio optimization. When volatility is constant, the transaction costs optimal investment problem has a long history, especially in the use of asymptotic approximations when the cost is small. Under stochastic volatility, but with no transaction costs, the Merton problem under general utility functions can also be analyzed with asymptotic methods. Here, we look at the long-run growth rate problem when both complexities are present, using separation of time scales approximations. This leads to perturbation analysis of an eigenvalue problem. We find the first term in the asymptotic expansion in the time scale parameter, of the optimal long-term growth rate, and of the optimal strategy, for fixed small transaction costs.Comment: 27 pages, 4 figure