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An asset manager's goal is to provide a high return relative the risk taken, and thus faces the challenge of how to choose an optimal portfolio. Many mathematical methods have been developed to achieve a good balance between these attributes and using di erent risk measures. In thisthesis, we test the use of a relatively simple and common approach: the Markowitz mean-variance method, and a more quantitatively demanding approach: the tail optimization method. Using active portfolio based on data provided by the Swedish fund management company Enter Fonderwe implement these approaches and compare the results. We analyze how each method weighs theunderlying assets in order to get an optimal portfolio.

Progress in the field of quantum computing has shown that, should construction of a sufficiently powerful quantum computer become feasible, much of the cryptography used on the Internet today will be rendered insecure. In lieu of this, several approaches to “quantum-safe” cryptography have been proposed, each one becoming a serious field of study. The youngest of these approaches, isogeny based cryptography, is oriented around problems in algebraic geometry involving a particular variety of elliptic curves. Supersingular isogeny Diffie-Hellman (SIDH) is this subfields main contender for quantum-safe key-exchange. Yoo et al. have provided an isogeny-based signature scheme built on top of SIDH. Currently, cryptographic algorithms in this class are hindered by poor performance metrics and, in the case of the Yoo et al. signature scheme, large communication overhead. In this dissertation we explore two different modifications to the implementation of this signature scheme; one with the intent of improving temporal performance, and another with the intent of reducing signature sizes. We show that our first modification, a mechanism for batching together expensive operations, can offer roughly 8% faster signature signing and verification. Our second modification, an adaptation of the SIDH public key compression technique outlined in [CJL + 17], can reduce Yoo et al. signature sizes from roughly 688λ bytes to 544λ bytes at the 128-bit security level on a 64-bit operating system. We also explore the combination of these techniques, and the potential of employing these techniques in different application settings. Our experiments reveal that isogeny based cryptosystems still have much potential for improved performance metrics. While some practitioners may believe isogeny-based cryptosystems impractical, we show that these systems still have room for improvement, and with continued research can be made more efficient - and eventually practical. Achieving more efficient implementations for quantum-safe algorithms will allow us to make them more accessible. With faster and lower-overhead implementations these primitives can be run on low bandwidth, low spec devices; ensuring that more and more machines can be made resistant to quantum cryptanalysis. / Thesis / Master of Science (MSc)

This paper gives an overview of differential placemarking phenomena and formulates a number of universals that seem to be well supported. Differential place marking is a situation in which the coding of locative, allative or ablative roles depends on subclasses of nouns, in particular place names (toponyms), inanimate common nouns and human nouns. When languages show asymmetric coding differences depending on such subclasses, they show shorter (and often zero) coding of place roles with toponyms, and longer (often adpositional rather than affixal) coding of place roles with human nouns. Like differential objectmarking, differential place marking can be explained by frequency asymmetries, expectations derived from frequencies, and the general preference for efficient coding. I also argue that differential place marking patterns provide an argument against the need to appeal to ambiguity avoidance to explain differential object marking.