\u3ci\u3eFrontier warfare: a series of ten lectures\u3c/i\u3e

The book is a series of the following ten tecture: General Principles; Frontier warfare camp; Measures for the security of a camp; Picquests protecting a camp; Marches; Protection on the march; Attack - defence - storming a fort; Pursuits and retreats, Base and line of communications - convoys; order

An Arbitrary Benchmark CAPM: One Additional Frontier Portfolio is Sufficient

The benchmark CAPM linearly relates the expected returns on an arbitrary asset, an arbitrary benchmark portfolio, and an arbitrary MV frontier portfolio. The benchmark is not required to be on the frontier and may be non-perfectly correlated with the frontier portfolio. The benchmark CAPM extends and generalizes previous CAPM formulations, including the zero beta, two correlated frontier portfolios, riskless augmented frontier, and inefficient portfolio versions. The covariance between the off-frontier benchmark and the frontier portfolio affects the systematic risk of any asset. Each asset has a composite beta, derived from the simple betas of both the asset and the benchmark.Benchmark; CAPM; non-frontier portfolio; zero beta portfolio; composite beta

The dimension of the Brownian frontier is greater than 1

Consider a planar Brownian motion run for finite time. The frontier or ``outer boundary'' of the path is the boundary of the unbounded component of the complement. Burdzy (1989) showed that the frontier has infinite length. We improve this by showing that the Hausdorff dimension of the frontier is strictly greater than 1. (It has been conjectured that the Brownian frontier has dimension $4/3$, but this is still open.) The proof uses Jones's Traveling Salesman Theorem and a self-similar tiling of the plane by fractal tiles known as Gosper Islands